finite mathematics and calculus with applications

This page intentionally left blank
Finite Mathematics
and Calculus with
Applications
NINTH EDITION
Margaret L. Lial
American River College
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Youngstown State University
Editor in Chief: Deirdre Lynch
Executive Editor: Jennifer Crum
Executive Content Editor: Christine O’Brien
Senior Project Editor: Rachel S. Reeve
Editorial Assistant: Joanne Wendelken
Senior Managing Editor: Karen Wernholm
Senior Production Project Manager: Patty Bergin
Associate Director of Design, USHE North and West: Andrea Nix
Senior Designer: Heather Scott
Digital Assets Manager: Marianne Groth
Media Producer: Jean Choe
Software Development: Mary Durnwald and Bob Carroll
Executive Marketing Manager: Jeff Weidenaar
Marketing Coordinator: Caitlin Crain
Senior Author Support/Technology Specialist: Joe Vetere
Rights and Permissions Advisor: Michael Joyce
Image Manager: Rachel Youdelman
Senior Manufacturing Buyer: Carol Melville
Senior Media Buyer: Ginny Michaud

Production Coordination and Composition: Nesbitt Graphics, Inc.
Illustrations: Nesbitt Graphics, Inc. and IllustraTech
Cover Design: Heather Scott
Cover Image: John Wollwerth/Shutterstock
Credits appear on page C-1, which constitutes a continuation of the copyright page.
Many of the designations used by manufacturers and sellers to distinguish their products are
claimed as trademarks. Where those designations appear in this book, and Pearson was aware of
a trademark claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Lial, Margaret L.
Finite mathematics and calculus with applications. — 9th
ed. / Margaret L. Lial, Raymond N. Greenwell, Nathan P.
Ritchey.
p.cm.
Includes bibliographical references and index.
ISBN-13: 978-0-321-74908-6
ISBN-10: 0-321-74908-1
1. Mathematics—Textbooks. 2. Calculus—Textbooks. I.
Greenwell, Raymond N. II. Ritchey, Nathan P. III. Title.
QA37.3.L54 2013
510—dc22
2010031432
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or
otherwise, without the prior written permission of the publisher. Printed in the United States of America. For information on
obtaining permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and
Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at
/>1 2 3 4 5 6 7 8 9 10—QG—15 14 13 12 11
ISBN-10: 0-321-74908-1
ISBN-13: 978-0-321-74908-6

NOTICE:
This work is
protected by U.S.
copyright laws and
is provided solely for
the use of college
instructors in review-
ing course materials
for classroom use.
Dissemination or sale
of this work, or any
part (including on the
World Wide Web), will
destroy the integrity
of the work and is
not permitted. The
work and materials
from it should never
be made available to
students except by
instructors using the
accompanying text in
their classes. All
recipients of this
work are expected to
abide by these
restrictions and to
honor the intended
pedagogical purposes
and the needs of

other instructors who
rely on these materi-
als.
www.pearsonhighered.com
Preface ix
Dear Student xxii
Prerequisite Skills Diagnostic Test xxiii
Algebra Reference R-1
Polynomials R-2
Factoring R-5
Rational Expressions R-8
Equations R-11
Inequalities R-16
Exponents R-21
Radicals R-25
Linear Functions 1
Slopes and Equations of Lines 2
Linear Functions and Applications 17
The Least Squares Line 25
CHAPTER 1 REVIEW 38
EXTENDED APPLICATION
Using Extrapolation to Predict Life Expectancy 42
Systems of Linear Equations and Matrices 44
Solution of Linear Systems by the Echelon Method 45
Solution of Linear Systems by the Gauss-Jordan Method 54
Addition and Subtraction of Matrices 70
Multiplication of Matrices 77
Matrix Inverses 87
Input-Output Models 97
CHAPTER 2 REVIEW 104

EXTENDED APPLICATION
Contagion 110
Linear Programming:The Graphical Method 112
Graphing Linear Inequalities 113
Solving Linear Programming Problems Graphically 120
Applications of Linear Programming 126
CHAPTER 3 REVIEW 134
EXTENDED APPLICATION
Sensitivity Analysis 137
3.3
3.2
3.1
2.6
2.5
2.4
2.3
2.2
2.1
1.3
1.2
1.1
R.7
R.6
R.5
R.4
R.3
R.2
R.1
iii
Contents

CHAPTER
R
CHAPTER
1
CHAPTER
2
CHAPTER
3
Linear Programming:The Simplex Method 142
Slack Variables and the Pivot 143
Maximization Problems 150
Minimization Problems; Duality 161
Nonstandard Problems 170
CHAPTER 4 REVIEW 179
EXTENDED APPLICATION
Using Integer Programming in the Stock-Cutting Problem 183
Mathematics of Finance 187
Simple and Compound Interest 188
Future Value of an Annuity 200
Present Value of an Annuity; Amortization 209
CHAPTER 5 REVIEW 218
EXTENDED APPLICATION
Time, Money, and Polynomials 222
Logic 224
Statements 225
Truth Tables and Equivalent Statements 233
The Conditional and Circuits 240
More on the Conditional 250
Analyzing Arguments and Proofs 257
Analyzing Arguments with Quantifiers 266

CHAPTER 6 REVIEW 274
EXTENDED APPLICATION
Logic Puzzles 279
Sets and Probability 283
Sets 284
Applications of Venn Diagrams 292
Introduction to Probability 302
Basic Concepts of Probability 311
Conditional Probability; Independent Events 322
Bayes’ Theorem 336
CHAPTER 7 REVIEW 343
EXTENDED APPLICATION
Medical Diagnosis 350
7.6
7.5
7.4
7.3
7.2
7.1
CHAPTER
6.6
6.5
6.4
6.3
6.2
6.1
CHAPTER
5.3
5.2
5.1

CHAPTER
4.4
4.3
4.2
4.1
CONTENTS
iv
5
6
7
CHAPTER
4
Counting Principles; Further Probability Topics 352
The Multiplication Principle; Permutations 353
Combinations 361
Probability Applications of Counting Principles 370
Binomial Probability 381
Probability Distributions; Expected Value 389
CHAPTER 8 REVIEW 400
EXTENDED APPLICATION
Optimal Inventory for a Service Truck 405
Statistics 407
Frequency Distributions; Measures of Central Tendency 408
Measures of Variation 419
The Normal Distribution 428
Normal Approximation to the Binomial Distribution 438
CHAPTER 9 REVIEW 445
EXTENDED APPLICATION
Statistics in the Law—The Castaneda Decision 449
Nonlinear Functions 452

Properties of Functions 453
Quadratic Functions;Translation and Reflection 465
Polynomial and Rational Functions 475
Exponential Functions 487
Logarithmic Functions 497
Applications: Growth and Decay; Mathematics of Finance 510
CHAPTER 10 REVIEW 518
EXTENDED APPLICATION
Power Functions 526
The Derivative 529
Limits 530
Continuity 548
Rates of Change 557
Definition of the Derivative 570
Graphical Differentiation 588
CHAPTER 11 REVIEW 594
EXTENDED APPLICATION
A Model for Drugs Administered Intravenously 601
11.5
11.4
11.3
11.2
11.1
10.6
10.5
10.4
10.3
10.2
10.1
9.4

9.3
9.2
9.1
8.5
8.4
8.3
8.2
8.1
CHAPTER
CHAPTER
CONTENTS
v
8
9
10
11
CHAPTER
CHAPTER
CONTENTS
vi
Calculating the Derivative 604
Techniques for Finding Derivatives 605
Derivatives of Products and Quotients 619
The Chain Rule 626
Derivatives of Exponential Functions 636
Derivatives of Logarithmic Functions 644
CHAPTER 12 REVIEW 651
EXTENDED APPLICATION
Electric Potential and Electric Field 656
Graphs and the Derivative 659

Increasing and Decreasing Functions 660
Relative Extrema 671
Higher Derivatives, Concavity, and the Second Derivative Test 682
Curve Sketching 695
CHAPTER 13 REVIEW 704
EXTENDED APPLICATION
A Drug Concentration Model for
Orally Administered Medications 708
Applications of the Derivative 711
Absolute Extrema 712
Applications of Extrema 721
Further Business Applications: Economic Lot Size; Economic Order Quantity;
Elasticity of Demand 730
Implicit Differentiation 739
Related Rates 744
Differentials: Linear Approximation 751
CHAPTER 14 REVIEW 757
EXTENDED APPLICATION
A Total Cost Model for a Training Program 761
Integration 763
Antiderivatives 764
Substitution 776
Area and the Definite Integral 784
The Fundamental Theorem of Calculus 796
The Area Between Two Curves 806
Numerical Integration 816
CHAPTER 15 REVIEW 824
EXTENDED APPLICATION
Estimating Depletion Dates for Minerals 829
15.6

15.5
15.4
15.3
15.2
15.1
CHAPTER
14.6
14.5
14.4
14.3
14.2
14.1
CHAPTER
13.4
13.3
13.2
13.1
CHAPTER
12.5
12.4
12.3
12.2
12.1
CHAPTER
13
14
15
12
Further Techniques and Applications of Integration 833
Integration by Parts 834

Volume and Average Value 842
Continuous Money Flow 849
Improper Integrals 856
Solution of Elementary and Separable Differential Equations 862
CHAPTER 16 REVIEW 875
EXTENDED APPLICATION
Estimating Learning Curves in
Manufacturing with Integrals 880
Multivariable Calculus 883
Functions of Several Variables 884
Partial Derivatives 895
Maxima and Minima 906
Lagrange Multipliers 915
Total Differentials and Approximations 923
Double Integrals 928
CHAPTER 17 REVIEW 939
EXTENDED APPLICATION
Using Multivariable Fitting to Create a
Response Surface Design 945
Probability and Calculus 949
Continuous Probability Models 950
Expected Value and Variance of Continuous Random Variables 961
Special Probability Density Functions 970
CHAPTER 18 REVIEW 982
EXTENDED APPLICATION
Exponential Waiting Times 987
Appendix
Solutions to Prerequisite Skills Diagnostic Test A-1
Learning Objectives A-4
MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition A-10

Tables A-12
1 Formulas from Geometry
2 Area Under a Normal Curve
3 Integrals
D
C
B
A
18.3
18.2
18.1
17.6
17.5
17.4
17.3
17.2
17.1
16.5
16.4
16.3
16.2
16.1
CONTENTS
vii
CHAPTER
CHAPTER
16
17
18
CHAPTER

Answers to Selected Exercises A-17
Credits C-1
Index of Applications I-1
Index I-7
Sources S-1
Special Topics to Accompany Finite Mathematics and Calculus with Applications
The following material is provided free to adopters at
www.pearsonhighered.com/mathstatsresources:
Digraphs and Networks
Graphs and Digraphs
Dominance Digraphs
Communication Digraphs
Networks
Review Exercises
CONTENTS
viii
Finite Mathematics and Calculus with Applications is a thorough, application-oriented text for
students majoring in business, management, economics, or the life or social sciences. In
addition to its clear exposition, this text consistently connects the mathematics to career and
everyday-life situations. A prerequisite of two years of high school algebra is assumed. A
renewed focus on quick and effective assessments, new applications and exercises, as well as
other new learning tools make this 9th edition an even richer learning resource for students.
Our Approach
Our main goal is to present finite mathematics and applied calculus in a concise and
meaningful way so that students can understand the full picture of the concepts they are
learning and apply it to real-life situations. This is done through a variety of ways.
Focus on Applications Making this course meaningful to students is critical to their
success. Applications of the mathematics are integrated throughout the text in the exposition,
the examples, the exercise sets, and the supplementary resources. Finite Mathematics and
Calculus with Applications presents students with a myriad of opportunities to relate what

they’re learning to career situations through the Apply It questions, the applied examples, and
the Extended Applications. To get a sense of the breadth of applications presented, look at
the Index of Applications in the back of the book or the extended list of sources of real-world
data on www.pearsonhighered.com/mathstatsresources.
Pedagogy to Support Students Students need careful explanations of the mathematics
along with examples presented in a clear and consistent manner. Additionally students and
instructors should have a means to assess the basic prerequisite skills. This can now be done
with the Prerequisite Skills Diagnostic Test located just before Chapter R. In addition, the stu-
dents need a mechanism to check their understanding as they go and resources to help them
remediate if necessary. Finite Mathematics and Calculus with Applications has this support
built into the pedagogy of the text through fully developed and annotated examples, Your
Turn exercises, For Review references, and supplementary material.
Beyond the Textbook Students today take advantage of a variety of resources and delivery
methods for instruction. As such, we have developed a robust MyMathLab course for Finite
Mathematics and Calculus with Applications. MyMathLab has a well-established and well-
documented track record of helping students succeed in mathematics. The MyMathLab
online course for Finite Mathematics and Calculus with Applications contains over 6700 exer-
cises to challenge students and provides help when they need it. Students who learn best by
seeing and hearing can view section- and example-level videos within MyMathLab or on the
book-specific DVD-Rom. These and other resources are available to students as a unified and
reliable tool for their success.
New to the Ninth Edition
Based on the authors’ experience in the classroom along with feedback from many
instructors across the country, the focus of this revision is to improve the clarity of the
presentation and provide students with more opportunities to learn, practice, and apply
what they’ve learned on their own. This is done in both the presentation of the content and
in new features added to the text.
Preface
ix
New and Revised Content

• Chapter R The flow of the material was improved by reordering some exercises and
examples. Exercises were added to Section R.1 (on performing algebraic operations) and
Section R.5 (on solving inequalities).
• Chapter 1 Changes in the presentation were made throughout to increase clarity, includ-
ing adding some examples and rewriting others. Terminology in Section 1.2 was adjusted
to be more consistent with usage in economics.
• Chapter 2 Section 2.1 was changed so that only systems of two equations are solved by
the echelon method, while systems with three or more equations are solved using the
Gauss-Jordan method in Section 2.2. The discussion of subtraction of matrices in Section 2.3
was simplified.
• Chapter 3 The concept of bounded and unbounded regions was moved from Section 3.2
to Section 3.1, where such regions are first encountered. An Extended Application on sensi-
tivity analysis was added to this chapter.
• Chapter 4 Exercises 25 through 30 in Section 4.1 were modified to clarify the role of slack
variables. Exercise 30 in Section 4.2 was modified to amplify how multiple solutions may
occur. The method for handling ties in nonstandard problems in Section 4.4 was improved.
• Chapter 5 In Section 5.1, examples and accompanying exercises were added covering how
to solve for the interest rate and how to find the compounding time, both with a graphing cal-
culator and with logarithms. The explanation of the rule of 70 and the rule of 72 was im-
proved. Material on continuous compounding was also added to Section 5.1. In Section 5.3,
an example and accompanying exercises were added on how a loan can be paid off early.
• Chapter 6 Many exercises in this chapter were revised so that the information would be more
relevant to students. For example, tax references include scholarships, tuition, paychecks,
reporting tips, filing taxes, inheritances, and tuition deductions. Law references include car
accidents, contracts, lawsuits, driver’s licenses, and marriage, and warranty references cover
iPhones and eBay. In Section 6.5, applications were revised to give more diversity in topics.
• Chapter 7 Empirical probability was moved from Section 7.4 to 7.3 so that methods for
determining probability are contained in the same section. In Section 7.4, probability distri-
butions are emphasized more and a probability distribution example was added. The intro-
duction to Bayes’ Theorem was rewritten for brevity and clarity in Section 7.6.

•
Chapter 8 The notation for combinations was changed from to to be more
current and consistent with our notation throughout the book. Section 8.3 now includes an
example illustrating probabilities using permutations and the multiplication principle.
• Chapter 9 In Section 9.1, a new example was added illustrating a case in which the
median is a truer representation of data than the mean.
• Chapter 10 The material in Section 10.1 on the Dow Jones Average was updated. Material
on even and odd functions was added. Material on identifying the degree of a polynomial
has been rewritten as an example to better highlight the concept. The discussion of the Rule
of 70 and the Rule of 72 was improved. A new Extended Application on Power Functions
has been added.
• Chapter 11 In Section 11.1, the introduction of limits was completely revised. The open-
ing discussion and example were transformed into a series of examples that progress
through different limit scenarios: a function defined at the limit, a function undefined at the
limit (a hole in the graph), a function defined at the limit but with a different value than the
limit (a piecewise function), and then finally, finding a limit when one does not exist. New
figures were added to illustrate the different scenarios. In Section 11.2 the definition and
example of continuity has been revised using a simple process to test for continuity. The
opening discussion of Section 11.5, showing how to sketch the graph of the derivative
given the graph of the original function, was rewritten as an example.
C
1
n, r
2
a
n
r
b
PREFACE
x

• Chapter 12 The introduction to the chain rule was rewritten as an example in Section 12.3.
Exercise topics were revised to cover subjects such as worldwide Internet users, online
learning, and the Gateway Arch.
• Chapter 13 In Section 13.1, the definition of increasing/decreasing functions has been
moved to the beginning of the chapter, followed by the discussion of using derivatives to
determine where the function increases and decreases. The determination of where a func-
tion is increasing or decreasing is divided into three examples: when the critical numbers are
found by setting the derivative equal to zero, when the critical numbers are found by deter-
mining where the derivative is undefined, and when the function has no critical numbers.
• Chapter 14 Changes in the presentation were made throughout to increase clarity and
exercise sets were rearranged to improve progression and parity.
•
Chapter 15 The social sciences category of exercises was added to Section 15.1, includ-
ing the topics of bachelor’s degrees and the number of females earning degrees in dentistry.
Color was added to the introduction and first example of substitution in Section 15.2 to
enable students to follow the substitution more easily.
•
Chapter 16 In addition to exercises based on real data being updated, examples in this
chapter were changed for pedagogical reasons.
• Chapter 17 Graphs generated by Maple™ were added to Examples 2 and 4 in Section 17.3
to assist students in visualizing the concept of relative extrema. Material covering utility
functions was added to Section 17.4. Many of the figures of three-dimensional surfaces were
improved to make them clearer and more attractive.
• Chapter 18 In Section 18.2, an example on how to calculate the probability within one
standard deviation of the mean (which is required in many of the exercises) was added. The
Social Sciences category was added to the exercise set, with exercises on calculating the
median, expected value, and standard deviation. Topics include the time it takes to learn a
task and the age of users of a social network.
Prerequisite Skills Diagnostic Test
The Prerequisite Skills Diagnostic Test gives students and instructors a means to assess the

basic prerequisite skills needed to be successful in this course. In addition, the answers to the
test include references to specific content in Chapter R as applicable so students can zero in
on where they need improvement. Solutions to the questions in this test are in Appendix A.
More Applications and Exercises
This text is used in large part because of the enormous amounts of real data used in examples and
exercises throughout the text. This 9th edition will not disappoint in this area. We have added or
updated more than 20% of the applications and 32% of the examples throughout the text and
added or updated more than 600 exercises.
Reference Tables for Exercises
The answers to odd-numbered exercises in the back of the textbook now contain a table
referring students to a specific example in the section for help with most exercises. For the
review exercises, the table refers to the section in the chapter where the topic of that exercise
is first discussed.
Annotated Instructor’s Edition
The annotated instructor’s edition is filled with valuable teaching tips in the margins for those
instructors who are new to teaching this course. In addition, answers to most exercises are
provided directly on the exercise set page along with + symbol next to the most challenging
exercises to make assigning and checking homework easier.
PREFACE
xi
New to MyMathLab
Available now with Finite Mathematics and Calculus with Applications are the following
resources within MyMathLab that will benefit students in this course.
• “Getting Ready for Finite Mathematics” and “Getting Ready for Applied
Calculus” chapters cover basic prerequisite skills
• Personalized Homework allows you to create homework assignments
based on the results of student assessments
• Videos with extensive section coverage
• Hundreds more assignable exercises than the previous edition of the text
• Application labels within exercise sets (e.g., “Bus/Econ”) make it easy for

you to find types of applications appropriate to your students
• Additional graphing calculator and Excel spreadsheet help
A detailed description of the overall capabilities of MyMathLab is provided
on page xviii.
PREFACE
xii
Source Lines
Sources for the exercises are now written in an abbreviated format within the actual exercise
so that students immediately see that the problem comes from, or pulls data from, actual
research or industry. The complete references are available at www.pearsonhighered.com/
mathstatsresources as well as on page S-1.
Other New Features
We have worked hard to meet the needs of today’s students through this revision. In addition
to the new content and resources listed above, there are many new features to this 9th edition
including new and enhanced examples, Your Turn exercises, the inclusion of and
instruction for new technology, and new and updated Extended Applications. You can
view these new features in context in the following Quick Walk-Through of Finite
Mathematics and Calculus with Applications, 9e.
xiii
A Quick Walk-Through of Finite Mathematics and Calculus with Applications, 9e
Mathematics of Finance
5.1 Simple and Compound Interest
5.2 Future Value of an Annuity
5.3 Present Value of an Annuity; Amortization
Chapter 5 Review
Extended Application:Time, Money,
and Polynomials
Buying a car usually requires both some savings for a down
payment and a loan for the balance. An exercise in Section 2
calculates the regular deposits that would be needed to

save up the full purchase price, and other exercises and
examples in this chapter compute the payments required
to amortize a loan.
5
Present Value of an Annuity; Amortization
What monthly payment will pay off a $17,000 car loan in 36 monthly
payments at 6% annual interest?
5.3
APPLY IT
The answer to this question is given in Example 2 in this section. We shall see that it
involves finding the present value of an annuity.
Suppose that at the end of each year, for the next 10 years, $500 is deposited in a sav-
ings account paying 7% interest compounded annually. This is an example of an ordinary
annuity. The present value of an annuity is the amount that would have to be deposited in
one lump sum today (at the same compound interest rate) in order to produce exactly the
same balance at the end of 10 years. We can find a formula for the present value of an annu-
ity as follows.
Suppose deposits of R dollars are made at the end of each period for n periods at inter-
est rate i per period. Then the amount in the account after n periods is the future value of
this annuity:
On the other hand, if P dollars are deposited today at the same compound interest rate i,
then at the end of n periods, the amount in the account is If P is the present value
of the annuity, this amount must be the same as the amount S in the formula above; that is,
To solve this equation for P, multiply both sides by
Use the distributive property; also recall that
The amount P is the present value of the annuity. The quantity in brackets is abbreviated as
so
(The symbol is read “a-angle-n at i.” Compare this quantity with in the previous
section.) The formula for the present value of an annuity is summarized on the next page.
s

n
0
i
a
n
0
i
a
n
0
i
5
1 2
1
1 1 i
2
2n
i
.
a

n
0
i
,
P 5 R
c
1
1 1 i

2
2n
1
1 1 i
2
n
2
1
1 1 i
2
2n
i
d
5 R
c
1 2
1
1 1 i
2
2n
i
d
1
1 1 i
2
2n
1
1 1 i
2
n

5 1.
P 5 R
1
1 1 i
2
2n
c
1
1 1 i
2
n
2 1
i
d
1
1 1 i
2
2n
.
P
1
1 1 i
2
n
5 R
c
1
1 1 i
2
n

2 1
i
d
.
P
1
1 1 i
2
n
.
S 5 R
.
s
n
0
i
5 R
c
1
1 1 i
2
n
2 1
i
d
.
FOR REVIEW
Recall from Section R.6 that for
any nonzero number a,
Also, by the product rule for

exponents, In par-
ticular, if a is any nonzero number
a
n
.
a
2n
5 a
n1
1
2n
2
5 a
0
5 1.
a
x
.
a
y
5 a
x1y
.
a
0
5 1.
Chapter Opener
Each chapter opens with a quick introduction that
relates to an application presented in the chapter.
In addition, a section-level table of contents is

included.
᭤
Apply It
An Apply It question, typically at the start of a sec-
tion, asks students to consider how to solve a real-
life situation related to the math they are about to
learn. The Apply It question is answered in an
application within the section or the exercise set.
(“Apply It” was labeled “Think About It” in the
previous edition.)
᭤
For Review
For Review boxes are provided in the margin as
appropriate, giving students just-in-time help
with skills they should already know but may
have forgotten. For Review comments sometimes
include an explanation while others refer students
back to earlier parts of the book for a more thorough
review.
NEW!
Teaching Tips
Teaching Tips are provided in the margins of the
Annotated Instructor’s Edition for those who are
new to teaching this course. In addition, answers
to most exercises are provided directly on the
exercise set page making it easier to assign and
check homework.
᭤
xiv
NEW!

“Your Turn” Exercises
The Your Turn exercises, following selected
examples, provide students with an easy way to
quickly stop and check their understanding of the
skill or concept being presented. Answers are
provided at the end of the section’s exercises.
᭤
᭤
᭤
Caution
Caution boxes provide students with a quick
“heads-up” to common student difficulties and
errors.
NEW!
Recognizing New Technology
Material on graphing calculators or Microsoft Excel™ is
now set off to make it easier for instructors to use this
material or not. All of the figures depicting graphing calcu-
lator screens have been redrawn to create a more accurate
depiction of the math. In addition, this edition references
and provides students with a transition to the new
MathPrint™ operating system of the TI-84 Plus through
the technology notes, a new appendix, and the Graphing
Calculator and Excel Spreadsheet Manual.
Note
Note boxes highlight and emphasize important treatments and asides.
NEW!
Enhanced Examples
Most learning from a textbook takes place within the
examples of the text. The authors have taken advantage

of this by adding more detailed annotations to the
already well-developed examples to guide students through
new concepts and skills.
᭤
Apply It
The solution to the Apply It question often falls in
the body of the text where it can be seen in context
with the mathematics.
᭤
᭤
xv
Exercises
Skill-based problems are followed by
application exercises, which are grouped by
subject with subheads indicating the specific
topic.
Connection exercises integrate topics pre-
sented in different sections or chapters and
are indicated with
Technology exercises are labeled with
for graphing calculator and for spreadsheet.
Writing exercises, labeled with provide
students with an opportunity to explain important
mathematical ideas.
Exercises that are particularly challenging are
denoted with
+ in the Annotated Instructor’s
Edition only.
᭤
5.3

Present Value of an Annuity; Amortization
215
1. Explain the difference between the present value of an annuity
and the future value of an annuity. For a given annuity, which
is larger? Why?
2. What does it mean to amortize a loan?
Find the present value of each ordinary annuity.
3. Payments of $890 each year for 16 years at 6% compounded
annually
4. Payments of $1400 each year for 8 years at 6% compounded
annually
5. Payments of $10,000 semiannually for 15 years at 5% com-
pounded semiannually
6. Payments of $50,000 quarterly for 10 years at 4% compounded
quarterly
7. Payments of $15,806 quarterly for 3 years at 6.8% com-
pounded quarterly
8. Payments of $18,579 every 6 months for 8 years at 5.4% com-
pounded semiannually
Find the lump sum deposited today that will yield the same
total amount as payments of $10,000 at the end of each year for
15 years at each of the given interest rates.
9. 4% compounded annually
10. 6% compounded annually
Find (a) the payment necessary to amortize each loan; (b) the
total payments and the total amount of interest paid based on the
calculated monthly payments, and (c) the total payments and
total amount of interest paid based upon an amortization table.
11. $2500; 6% compounded quarterly; 6 quarterly payments
12. $41,000; 8% compounded semiannually; 10 semiannual

payments
13. $90,000; 6% compounded annually; 12 annual payments
14. $140,000; 8% compounded quarterly; 15 quarterly payments
15. $7400; 6.2% compounded semiannually; 18 semiannual payments
16. $5500; 10% compounded monthly; 24 monthly payments
Suppose that in the loans described in Exercises 13–16, the bor-
rower paid off the loan after the time indicated below. Calculate
the amount needed to pay off the loan, using either of the two
methods described in Example 4.
17. After 3 years in Exercise 13
18. After 5 quarters in Exercise 14
19. After 3 years in Exercise 15
20. After 7 months in Exercise 16
Use the amortization table in Example 5 to answer the ques-
tions in Exercises 21–24.
21. How much of the fourth payment is interest?
22. How much of the eleventh payment is used to reduce the debt?
5.3 EXERCISES
23. How much interest is paid in the first 4 months of the loan?
24. How much interest is paid in the last 4 months of the loan?
25. What sum deposited today at 5% compounded annually for 8
years will provide the same amount as $1000 deposited at the
end of each year for 8 years at 6% compounded annually?
26. What lump sum deposited today at 8% compounded quarterly
for 10 years will yield the same final amount as deposits of
$4000 at the end of each 6-month period for 10 years at 6%
compounded semiannually?
Find the monthly house payments necessary to amortize each
loan. Then calculate the total payments and the total amount
of interest paid.

27. $199,000 at 7.01% for 25 years
28. $175,000 at 6.24% for 30 years
29. $253,000 at 6.45% for 30 years
30. $310,000 at 5.96% for 25 years
Suppose that in the loans described in Exercises 13–16, the bor-
rower made a larger payment, as indicated below. Calculate (a)
the time needed to pay off the loan, (b) the total amount of the
payments, and (c) the amount of interest saved, compared with
part c of Exercises 13–16.
31. $16,000 in Exercise 13
32. $18,000 in Exercise 14
33. $850 in Exercise 15
34. $400 in Exercise 16
APPLICATIONS
Business and Economics
35. House Payments Calculate the monthly payment and total
amount of interest paid in Example 3 with a 15-year loan, and
then compare with the results of Example 3.
36. Installment Buying Stereo Shack sells a stereo system for
$600 down and monthly payments of $30 for the next 3 years. If
the interest rate is 1.25% per month on the unpaid balance, find
a. the cost of the stereo system.
b. the total amount of interest paid.
37. Car Payments Hong Le buys a car costing $14,000. He
agrees to make payments at the end of each monthly period for
4 years. He pays 7% interest, compounded monthly.
a. What is the amount of each payment?
b. Find the total amount of interest Le will pay.
38. Credit Card Debt Tom Shaffer charged $8430 on his credit
card to relocate for his first job. When he realized that the

interest rate for the unpaid balance was 27% compounded
monthly, he decided not to charge any more on that account.
He wants to have this account paid off by the end of 3 years,
5.3
Present Value of an Annuity; Amortization
217
48. Loan Payments When Nancy Hart opened her law office,
she bought $14,000 worth of law books and $7200 worth of
office furniture. She paid $1200 down and agreed to amortize
the balance with semiannual payments for 5 years, at 8% com-
pounded semiannually.
a. Find the amount of each payment.
b. Refer to the text and Figure 13. When her loan had been
reduced below $5000, Nancy received a large tax refund and
decided to pay off the loan. How many payments were left at
this time?
49. House Payments Ian Desrosiers buys a house for $285,000.
He pays $60,000 down and takes out a mortgage at 6.5% on
the balance. Find his monthly payment and the total amount of
interest he will pay if the length of the mortgage is
a. 15 years;
b. 20 years;
c. 25 years.
d. Refer to the text and Figure 13. When will half the 20-year
loan in part b be paid off?
50. House Payments The Chavara family buys a house for
$225,000. They pay $50,000 down and take out a 30-year
mortgage on the balance. Find their monthly payment and the
total amount of interest they will pay if the interest rate is
a. 6%;

b. 6.5%;
c. 7%.
d. Refer to the text and Figure 13. When will half the 7% loan
in part c be paid off?
51. Refinancing a Mortgage Fifteen years ago, the Budai family
bought a home and financed $150,000 with a 30-year mortgage
at 8.2%.
a. Find their monthly payment, the total amount of their pay-
ments, and the total amount of interest they will pay over the
life of this loan.
b. The Budais made payments for 15 years. Estimate the
unpaid balance using the formula
,
and then calculate the total of their remaining payments.
c. Suppose interest rates have dropped since the Budai family
took out their original loan. One local bank now offers a
30-year mortgage at 6.5%. The bank fees for refinancing are
$3400. If the Budais pay this fee up front and refinance the
balance of their loan, find their monthly payment. Including
the refinancing fee, what is the total amount of their pay-
ments? Discuss whether or not the family should refinance
with this option.
y 5 R
c
1 2
1
1 1 i
2
2
1

n2x
2
i
d
d. A different bank offers the same 6.5% rate but on a 15-year
mortgage. Their fee for financing is $4500. If the Budais pay
this fee up front and refinance the balance of their loan, find
their monthly payment. Including the refinancing fee, what
is the total amount of their payments? Discuss whether or
not the family should refinance with this option.
52. Inheritance Deborah Harden has inherited $25,000 from her
grandfather’s estate. She deposits the money in an account
offering 6% interest compounded annually. She wants to make
equal annual withdrawals from the account so that the money
(principal and interest) lasts exactly 8 years.
a. Find the amount of each withdrawal.
b. Find the amount of each withdrawal if the money must last
12 years.
53. Charitable Trust The trustees of a college have accepted a
gift of $150,000. The donor has directed the trustees to deposit
the money in an account paying 6% per year, compounded
semiannually. The trustees may make equal withdrawals at the
end of each 6-month period; the money must last 5 years.
a. Find the amount of each withdrawal.
b. Find the amount of each withdrawal if the money must last
6 years.
Amortization Prepare an amortization schedule for each
loan.
54. A loan of $37,948 with interest at 6.5% compounded annually,
to be paid with equal annual payments over 10 years.

55. A loan of $4836 at 7.25% interest compounded semi-annually,
to be repaid in 5 years in equal semiannual payments.
56. Perpetuity A perpetuity is an annuity in which the payments
go on forever. We can derive a formula for the present value of
a perpetuity by taking the formula for the present value of an
annuity and looking at what happens when n gets larger
and larger. Explain why the present value of a perpetuity is
given by
57. Perpetuity Using the result of Exercise 56, find the present
value of perpetuities for each of the following.
a. Payments of $1000 a year with 4% interest compounded
annually
b. Payments of $600 every 3 months with 6% interest com-
pounded quarterly
P 5
R
i
.
YOUR TURN ANSWERS
1. $6389.86 2. $394.59
3. $1977.42, $135,935.60 4. $679.84
.
,
xvi
End-of-Chapter Summary
End-of-Chapter Summary provides students
with a quick summary of the key ideas of the
chapter followed by a list of key definitions, terms,
and examples.
᭤

Extended Applications
Extended Applications are provided now at
the end of every chapter as in-depth applied
exercises to help stimulate student interest.
These activities can be completed individually
or as a group project.
CHAPTER 5
Mathematics of Finance
220
15. For a given amount of money at a given interest rate for a given
time period, does simple interest or compound interest produce
more interest?
Find the compound amount in each loan.
16. $2800 at 7% compounded annually for 10 years
17. $19,456.11 at 8% compounded semiannually for 7 years
18. $312.45 at 5.6% compounded semiannually for 16 years
19. $57,809.34 at 6% compounded quarterly for 5 years
Find the amount of interest earned by each deposit.
20. $3954 at 8% compounded annually for 10 years
21. $12,699.36 at 5% compounded semiannually for 7 years
22. $12,903.45 at 6.4% compounded quarterly for 29 quarters
23. $34,677.23 at 4.8% compounded monthly for 32 months
24. What is meant by the present value of an amount A?
Find the present value of each amount.
25. $42,000 in 7 years, 6% compounded monthly
26. $17,650 in 4 years, 4% compounded quarterly
27. $1347.89 in 3.5 years, 6.77% compounded semiannually
28. $2388.90 in 44 months, 5.93% compounded monthly
29 Write the first five terms of the geometric sequence with a
5

2
43. $11,900 deposited at the beginning of each month for 13 months;
money earns 6% compounded monthly.
44. What is the purpose of a sinking fund?
Find the amount of each payment that must be made into a
sinking fund to accumulate each amount.
45. $6500; money earns 5% compounded annually for 6 years.
46. $57,000; money earns 4% compounded semiannually for
years.
47. $233,188; money earns 5.2% compounded quarterly for years.
48. $1,056,788; money earns 7.2% compounded monthly for years.
Find the present value of each ordinary annuity.
49. Deposits of $850 annually for 4 years at 6% compounded
annually
50. Deposits of $1500 quarterly for 7 years at 5% compounded
quarterly
51. Payments of $4210 semiannually for 8 years at 4.2% com-
pounded semiannually
52. Payments of $877.34 monthly for 17 months at 6.4% com-
pounded monthly
53. Give two examples of the types of loans that are commonly
amortized.
Find the amount of the payment necessary to amortize each
4
1
2
7
3
4
8

1
2
Chapter Review Exercises
Chapter Review Exercises have been slightly
reorganized so that the Concept Check exercises
fall within the Chapter Review Exercises. This
provides students with a more complete review
of both the skills and the concepts they should
have mastered in this chapter. These exercises in
their entirety provide a comprehensive review for
a chapter-level exam.
᭤
TIME, MONEY, AND POLYNOMIALS*
A
time line is often
helpful for evaluating
complex investments.
For example, suppose you
buy a $1000 CD at time
After one year $2500 is
added to the CD at By time
after another year, your
money has grown to $3851
with interest. What rate of
interest, called yield to matu-
rity (YTM), did your money
earn? A time line for this situ-
ation is shown in Figure 15.
t
2

,
t
1
.
t
0
.
Assuming interest is compounded annually at a rate i, and using the
compo nd interest form la gi es the follo ing description of the YTM
time
$1000 $2500
$3851
t
2
t
1
t
0
FIGURE 15
To determine the yield to maturity, we must solve this equation for
i. Since the quantity is repeated, let and first solve
the second-degree (quadratic) polynomial equation for x.
We can use the quadratic formula with and
We get and Since the two
values for i are and We
reject the negative value because the final accumulation is greater
than the sum of the deposits. In some applications, however, nega-
tive rates may be meaningful. By checking in the first equation, we
see that the yield to maturity for the CD is 7.67%.
Now let us consider a more complex but realistic problem. Sup-

pose Austin Caperton has contributed for 4 years to a retirement fund.
He contributed $6000 at the beginning of the first year. At the begin-
ning of the next 3 years, he contributed $5840, $4000, and $5200,
respectively. At the end of the fourth year, he had $29,912.38 in his
fund. The interest rate earned by the fund varied between 21% and
so Caperton would like to know the for his hard-
earned retirement dollars. From a time line (see Figure 16), we set up
th f ll i ti i f C t ’ i1 1 i
YTM 5 i23%,
2457.67%.24.5767 50.0767 5 7.67%
x 5 1 1 i,x 523.5767.x 5 1.0767
x 5
22500 6 "2500
2
2 4
1
1000
21
23851
2
2
1
1000
2
c 523851.
b 5 2500,a 5 1000,
1000x
2
1 2500x 2 3851 5 0
x 5 1 1 i1 1 i

EXTENDED APPLICATION
Determine whether each of the following statements is true or
false, and explain why.
1. For a particular interest rate, compound interest is always bet-
ter than simple interest.
2. The sequence 1, 2, 4, 6, 8, . . . is a geometric sequence.
3. If a geometric sequence has first term 3 and common ratio 2,
then the sum of the first 5 terms is .
4. The value of a sinking fund should decrease over time.
5. For payments made on a mortgage, the (noninterest) portion of
the payment applied on the principal increases over time.
6. On a 30-year conventional home mortgage, at recent interest
rates, it is common to pay more money on the interest on the
loan than the actual loan itself.
7. One can use the amortization payments formula to calculate
the monthly payment of a car loan.
8. The effective rate formula can be used to calculate the present
value of a loan.
S
5
5 93
REVIEW EXERCISES
CONCEPT CHECK
9. The following calculation gives the monthly payment on a
$25,000 loan, compounded monthly at a rate of 5% for a
period of six years:
10. The following calculation gives the present value of an annu-
ity of $5,000 payments at the end of each year for 10 years.
The fund earns 4.5% compounded annually.
Find the simple interest for each loan.

11. $15,903 at 6% for 8 months
12. $4902 at 5.4% for 11 months
13. $42,368 at 5.22% for 7 months
14. $3478 at 6.8% for 88 days (assume a 360-day year)
5000
c
1 2
1
1.045
2
210
0.045
d
25,000
c
1
1 1 0.05
/
12
2
72
2 1
0.05
/
12
d
.
PRACTICE AND EXPLORATION
᭤
PREFACE

xvii
Flexible Syllabus
The flexibility of the text is indicated in the following chart of chapter prerequisites. As
shown, the course could begin with either Chapter 1 or Chapter 7. Chapter 5 on the mathe-
matics of finance and Chapter 6 on logic could be covered at any time, although Chapter 6
makes a nice introduction to ideas covered in Chapter 7.
CHAPTER 1:
Linear Functions
CHAPTER 9:
Statistics
CHAPTERS 10–18:
Calculus
CHAPTER 5:
Mathematics of
Finance
CHAPTER 6:
Logic
CHAPTER 8:
Counting Principles;
Further Probability
Topics
CHAPTER 7:
Sets and Probability
CHAPTER 2:
Systems of Linear
Equations and Matrices
CHAPTER 3:
Linear Programming:
The Graphical Method
CHAPTER 4:

Linear Programming:
The Simplex Method
PREFACE
xviii
Video Lectures on DVD-ROM with Optional Captioning
• Complete set of digitized videos, with extensive section
coverage, for student use at home or on campus
• Ideal for distance learning or supplemental instruction
• ISBN 0-321-74612-0 / 978-0-321-74612-2
Supplementary Content
• Digraphs and Networks
• Additional Extended Applications
• Comprehensive source list
• Available at the Downloadable Student Resources site,
www.pearsonhighered.com/mathstatsresources, and to
qualified instructors within MyMathLab or through the
Pearson Instructor Resource Center,
www.pearsonhighered.com/irc
Supplements
STUDENT RESOURCES INSTRUCTOR RESOURCES
Annotated Instructor’s Edition
• Numerous teaching tips
• Includes all the answers, usually on the same page as
the exercises, for quick reference
• More challenging exercises are indicated with a + symbol
• ISBN 0-321-75798-X / 978-0-321-75798-2
Instructor’s Resource Guide and Solutions Manual
(download only)
• Provides complete solutions to all exercises, two
versions of a pre-test and final exam, and teaching

tips.
• Authored by Elka Block and Frank Purcell
• Available to qualified instructors within MyMathLab or
through the Pearson Instructor Resource Center,
www.pearsonhighered.com/irc
PowerPoint Lecture Presentation
• Newly revised and greatly improved
• Classroom presentation slides are geared specifically to
the sequence and philosophy of this textbook.
• Includes lecture content and key graphics from the book
• Available to qualified instructors within MyMathLab or
through the Pearson Instructor Resource Center,
www.pearsonhighered.com/irc
• Authored by Dr. Sharda K. Gudehithlu, Wilbur Wright
College
Student Edition
• ISBN 0-321-74908-1 / 978-0-321-74908-6
Student’s Solutions Manual
• Provides detailed solutions to all odd-numbered text
exercises and sample chapter tests with answers.
• Authored by Elka Block and Frank Purcell
• ISBN 0-321-74623-6 / 978-0-321-74623-8
Graphing Calculator and Excel Spreadsheet Manual
• Provides instructions and keystroke operations for the
TI-83/84 Plus, the TI-84 Plus with the new operating
system featuring MathPrint™, and the TI-89 as well as
for the Excel spreadsheet program.
• Authored by GEX Publishing Services
• ISBN 0-321-70966-7 / 978-0-321-70966-0
MyMathLab

®
Online Course (access code required)
www.mymathlab.com
MyMathLab delivers proven results in helping individual students succeed.
• MyMathLab has a consistently positive impact on the quality of learning in higher
education math instruction. MyMathLab can be successfully implemented in any
environment—lab-based, hybrid, fully online, traditional—and demonstrates the
quantifiable difference that integrated usage has on student retention, subsequent
success, and overall achievement.
• MyMathLab’s comprehensive online gradebook automatically tracks your students’
results on tests, quizzes, homework, and in the study plan. You can use the gradebook
to quickly intervene if your students have trouble, or to provide positive feedback on
a job well done. The data within MyMathLab is easily exported to a variety of spread-
sheet programs, such as Microsoft Excel. You can determine which points of data you
want to export, and then analyze the results to determine success.
Media Resources
PREFACE
xix
MyMathLab provides engaging experiences that personalize, stimulate, and measure learning
for each student.
• Tutorial Exercises: The homework and practice exercises in MyMathLab are correlated
to the exercises in the textbook, and they regenerate algorithmically to give students
unlimited opportunity for practice and mastery. The software offers immediate, helpful
feedback when students enter incorrect answers.
• Multimedia Learning Aids: Exercises include guided solutions, sample problems, Inter-
active Figures, animations, videos, and the complete eText for extra help at point-of-use.
• Expert Tutoring: Although many students describe the whole of MyMathLab as “like
having your own personal tutor,” students using MyMathLab do have access to live
tutoring from Pearson, from qualified math and statistics instructors who provide
tutoring sessions for students via MyMathLab.

And, MyMathLab comes from a trusted partner with educational expertise and an eye on
the future.
Knowing that you are using a Pearson product means knowing that you are using qual-
ity content. That means that our eTexts are accurate, that our assessment tools work,
and that our questions are error-free. And whether you are just getting started with
MyMathLab, or have a question along the way, we’re here to help you learn about our
technologies and how to incorporate them into your course.
To learn more about how MyMathLab combines proven learning applications with powerful
assessment, visit www.mymathlab.com or contact your Pearson representative.
MathXL
®
Online Course (access code required)
www.mathxl.com
MathXL
®
is the homework and assessment engine that runs MyMathLab. (MyMathLab is
MathXL plus a learning management system.) With MathXL, instructors can:
• Create, edit, and assign online homework and tests using algorithmically generated
exercises correlated at the objective level to the textbook.
• Create and assign their own online exercises and import TestGen tests for added
flexibility.
• Maintain records of all student work tracked in MathXL’s online gradebook.
With MathXL, students can:
• Take chapter tests in MathXL and receive personalized study plans and/or personalized
homework assignments based on their test results.
• Use the study plan and/or the homework to link directly to tutorial exercises for the
objectives they need to study.
• Access supplemental animations and video clips directly from selected exercises.
MathXL is available to qualified adopters. For more information, visit our website at
www.mathxl.com, or contact your Pearson representative.

TestGen
®
www.pearsoned.com/testgen
TestGen
®
enables instructors to build, edit, print, and administer tests using a computerized
bank of questions developed to cover all the objectives of the text. TestGen is algorithmically
based, allowing instructors to create multiple but equivalent versions of the same question or
test with the click of a button. Instructors can also modify test bank questions or add new
questions. The software and testbank are available for download from Pearson Education’s
online catalog.
Acknowledgments We wish to thank the following professors for their contributions in reviewing portions of
this text:
Lowell Abrams, The George Washington University
John Alford, Sam Houston State University
Nathan Borchelt, Clayton State University
Robert David Borgersen, University of Manitoba
Joanne Brunner, Joliet Junior College
C.T. Bruns, University of Colorado, Boulder
James K. Bryan, Jr., Merced College
Nurit Budinsky, University of Massachusetts—Dartmouth
James Carolan, Wharton County Junior College
Martha Morrow Chalhoub, Collin College
Karabi Datta, Northern Illinois University
Michelle DeDeo, University of North Florida
James “Rob” Ely, Blinn College—Bryan Campus
Sam Evers, The University of Alabama
Kevin Farrell, Lyndon State College
Chris Ferbrache, Fresno City College
Lauren Fern, University of Montana

Pete Gomez, Houston Community College, Northwest
Sharda K. Gudehithlu, Wilbur Wright College
Mary Beth Headlee, State College of Florida
Yvette Hester, Texas A & M University
David L. Jones, University of Kansas
Karla Karstens, University of Vermont
Monika Keindl, Northern Arizona University
Lynette J. King, Gadsden State Community College
Jason Knapp, University of Virginia
Donna S. Krichiver, Johnson County Community College
Mark C. Lammers, University of North Carolina, Wilmington
Lia Liu, University of Illinois at Chicago
Donna M. Lynch, Clinton Community College
Rebecca E. Lynn, Colorado State University
Rodolfo Maglio, Northeastern Illinois University
Cyrus Malek, Collin College
Phillip Miller, Indiana University Southeast
Marna Mozeff, Drexel University
Javad Namazi, Fairleigh Dickinson University
Bishnu Naraine, St. Cloud State University
Dana Nimic, Southeast Community College—Lincoln
Lisa Nix, Shelton State Community College
Sam Northshield, SUNY, Plattsburgh
Charles Odion, Houston Community College
Susan Ojala, University of Vermont
Charles B. Pierre, Clark Atlanta University
Stela Pudar-Hozo, Indiana University Northwest
Brooke Quinlan, Hillsborough Community College
Candace Rainer, Meridian Community College
Nancy Ressler, Oakton Community College

Arthur J. Rosenthal, Salem State College
Theresa Rushing, The University of Tennessee at Martin
Katherine E. Schultz, Pensacola Junior College
Barbara Dinneen Sehr, Indiana University, Kokomo
Gordon H. Shumard, Kennesaw State University
PREFACE
xx
Walter Sizer, Minnesota State University, Moorhead
Mary Alice Smeal, Alabama State University
Alexis Sternhell, Delaware County Community College
Jennifer Strehler, Oakton Community College
Antonis P. Stylianou, University of Missouri—Kansas City
Darren Tapp, Hesser College
Jason Terry, Central New Mexico Community College
Yan Tian, Palomar College
Sara Van Asten, North Hennepin Community College
Amanda Wheeler, Amarillo College
Douglas Williams, Arizona State University
Roger Zarnowski, Angelo State University
We also thank Elka Block and Frank Purcell of Twin Prime Editorial for doing an excellent
job updating the Student’s Solutions Manual and Instructor’s Resource Guide and Solutions
Manual, an enormous and time-consuming task. Further thanks go to our accuracy
checkers Renato Mirollo, Jon Weerts, Tom Wegleitner, Nathan Kidwell, John Samons, and
Lauri Semarne. We are very thankful for the work of William H. Kazez, Theresa Laurent,
and Richard McCall, in writing Extended Applications for the book. We are grateful to
Karla Harby and Mary Ann Ritchey for their editorial assistance. We especially appreciate
the staff at Pearson, whose contributions have been very important in bringing this project
to a successful conclusion.
Margaret L. Lial
Raymond N. Greenwell

Nathan P. Ritchey
PREFACE
xxi
xxii
Dear Student,
Hello! The fact that you’re reading this preface is good news. One of the keys to suc-
cess in a math class is to read the book. Another is to answer all the questions correctly
on your professor’s tests. You’ve already started doing the first; doing the second may
be more of a challenge, but by reading this book and working out the exercises, you’ll
be in a much stronger position to ace the tests. One last essential key to success is to go
to class and actively participate.
You’ll be happy to discover that we’ve provided the answers to the odd-numbered exer-
cises in the back of the book. As you begin the exercises, you may be tempted to imme-
diately look up the answer in the back of the book, and then figure out how to get that
answer. It is an easy solution that has a consequence—you won’t learn to do the exer-
cises without that extra hint. Then, when you take a test, you will be forced to answer
the questions without knowing what the answer is. Believe us, this is a lot harder! The
learning comes from figuring out the exercises. Once you have an answer, look in the
back and see if your answer agrees with ours. If it does, you’re on the right path. If it
doesn’t, try to figure out what you did wrong. Once you’ve discovered your error, con-
tinue to work out more exercises to master the concept and skill.
Equations are a mathematician’s way of expressing ideas in concise shorthand. The prob-
lem in reading mathematics is unpacking the shorthand. One useful technique is to read
with paper and pencil in hand so you can work out calculations as you go along. When
you are baffled, and you wonder, “How did they get that result?” try doing the calculation
yourself and see what you get. You’ll be amazed (or at least mildly satisfied) at how often
that answers your question. Remember, math is not a spectator sport. You don’t learn
math by passively reading it or watching your professor. You learn mathematics by doing
mathematics.
Finally, if there is anything you would like to see changed in the book, feel free to write to

us at or We’re constantly trying to make this
book even better. If you’d like to know more about us, we have Web sites that we invite
you to visit: and />Marge Lial
Ray Greenwell
Nate Ritchey
Prerequisite Skills Diagnostic Test
Below is a very brief test to help you recognize which, if any, prerequisite skills you may
need to remediate in order to be successful in this course. After completing the test,
check your answers in the back of the book. In addition to the answers, we have also pro-
vided the solutions to these problems in Appendix A. These solutions should help remind
you how to solve the problems. For problems 5-26, the answers are followed by refer-
ences to sections within Chapter R where you can find guidance on how to solve the
problem and/or additional instruction. Addressing any weak prerequisite skills now will
make a positive impact on your success as you progress through this course.
1. What percent of 50 is 10?
2. Simplify
3. Let x be the number of apples and y be the number of oranges. Write the following state-
ment as an algebraic equation: “The total number of apples and oranges is 75.”
4. Let s be the number of students and p be the number of professors. Write the following
statement as an algebraic equation: “There are at least four times as many students as
professors.”
5. Solve for k:
6. Solve for x:
7. Write in interval notation:
8. Using the variable x, write the following interval as an inequality:
9. Solve for y:
10. Solve for
11. Carry out the operations and simplify:
12. Multiply out and simplify
13. Multiply out and simplify

14. Factor .
15. Factor 3x
2
2 x 2 10.
3pq 1 6p
2
q 1 9pq
2
1
a 2 2b
2
2
.
1
x
2
2 2x 1 3
2

1
x 1 1
2
.
1
5y
2
2 6y 2 4
2
2 2
1

3y
2
2 5y 1 1
2
.
p:
2
3
1
5p 2 3
2
.
3
4
1
2p 1 1
2
.
5
1
y 2 2
2
1 1 # 7y 1 8.
1
2`, 23
4
.
22 , x # 5.
5
8

x 1
1
16
x 5
11
16
1 x.
7k 1 8 524
1
3 2 k
2
.
13
7
2
2
5
.
xxiii