Soo t tan college mathematics for the managerial, life, and social sciences, (7th edition) cengage learning (2007)

LIST OF APPLICATIONS
BUSINESS AND ECONOMICS
Access to capital, 476
Accumulated value of an income stream, 1012
Accumulation years of baby boomers, 721
Adjustable-rate mortgage, 318
Advertising, 56, 180, 182, 183, 192, 195, 235, 254,
370, 488, 759, 1057, 1060
Ailing financial institutions, 653, 671
Aircraft structural integrity, 783
Airfone usage, 440
Airline safety, 396
Airport traffic, 1042
Air travel, 904
Allocation of funds 181, 194, 271
Allocation of services, 517
Alternative energy sources, 975
Alternative minimum tax, 805, 861
Amusement park attendance, 720, 1011
Annual retail sales, 620, 678
Annuities, 298, 300, 302, 304, 905, 984, 989
Assembly-time studies, 387, 394, 406, 802, 804, 897,
949
Asset allocation, 181, 182, 194, 235, 236, 405
ATM cards, 358
Auditing tax returns, 426
Authentication technology, 61
Auto financing, 959
Automobile leasing, 304, 333
Auto replacement parts market, 614

Average age of cars in U.S., 824
Average price of a commodity, 963, 1003
Balloon payment mortgage, 317
Banking, 116, 584, 671, 919
Bidding for contracts, 371
Bidding for rights, 549
Black Monday, 809
BlackBerry subscribers, 612
Book design, 616, 847
Bookstore inventories, 116
Box-office receipts, 78, 93, 131, 638, 705, 820
Brand selection, 413
Break-even analysis, 44, 53
Bridge loans, 289
Broadband Internet households, 37, 589
Broadband versus dial-up, 50
Budget deficit and surplus, 596, 776
Business spending on technology, 805
Business travel expenses, 93
Buying trends of home buyers, 531
Cable ad revenue, 620
Cable TV subscription, 465, 768, 932, 962
Calling cards, 61
Capital expenditures, 144, 316, 333
Capital value, 1035
Cargo volume, 790
Cash reserves at Blue Cross and Blue Shield, 806
CDs, 333
Cellular phone subscription, 786
Charter revenue, 610, 616, 848

Chip sales, 612
City planning, 515, 516, 642, 706
Coal production, 961, 1003
Cobb–Douglas production function, 1066, 1071, 1096,
1113
COLAs, 329, 589
Commissions, 654
Commodity prices, 654, 682, 882, 902, 1003
Common stock transactions, 165, 290, 386, 570
Commuter airlines, 1002

Compact disc sales, 1003
Company sales, 68, 323, 326, 330
Complimentary commodities, 1067, 1072
Computer-aided court transcription, 540
Computer game sales, 1049
Computer resale value, 994
Computer sales projections, 930
Consolidation of business loans, 290
Construction costs, 616
Construction jobs, 604
Consumer demand, 608, 705, 763, 908
Consumer price index, 693, 797, 907
Consumption functions, 36, 589
Consumption of electricity, 949
Consumption of petroleum, 1023
Corporate bonds, 290
Cost of drilling, 329
Cost of laying cable, 4, 8
Cost of producing DVDs, 769, 820

Cost of producing guitars, 920
Cost of producing loudspeakers, 827
Cost of producing PDAs, 603
Cost of producing solar cell panels, 928
Cost of producing surfboards, 674
Cost of removing toxic waste, 705, 820
Cost of wireless phone calls, 769
Creation of new jobs, 719
Credit card debt, 613, 921
Credit cards, 333, 376
Cruise ship bookings, 506, 719
Custodial accounts, 989
Customer service, 387, 488
Customer surveys, 440, 451
Decision analysis, 45, 49
Demand for agricultural commodities, 763
Demand for butter, 1045
Demand for commodities, 615
Demand for computer software, 1049
Demand for digital camcorder tapes, 995
Demand for DVD players, 614, 908
Demand for electricity, 40, 41, 63, 949
Demand for perfume, 881
Demand for personal computers, 719, 901
Demand for RNs, 803
Demand for wine, 882
Demand for wristwatches, 705, 719
Depletion of Social Security funds, 839
Depreciation, 31, 589, 879, 962
Designing a cruise ship pool, 1020

Determining the optimal site, 1084
Dial-up Internet households, 37
Digital camera sales, 692
Digital TV sales, 804
Digital TV services, 22
Digital TV shipments, 620
Digital versus film cameras, 50
Disability benefits, 741
Disposable annual incomes, 611
Document management, 613
Double-declining balance depreciation, 327, 330
Downloading music, 405
Driving costs, 607, 638, 678
Drug spending, 805
Durable goods orders, 393
DVD sales, 700, 921
Economic surveys, 351
Effect of advertising on bank deposits, 802
Effect of advertising on hotel revenue, 805
Effect of advertising on profit, 674, 763

Effect of advertising on revenue, 974
Effect of advertising on sales, 612, 693, 759, 763, 797,
853, 901, 975
Effect of housing starts on jobs, 719
Effect of inflation on salaries, 291
Effect of luxury tax on consumption, 718
Effect of mortgage rates on housing starts, 603, 763
Effect of price increase on quantity demanded, 754,
766

Effect of speed on operating cost of a truck, 759
Effect of TV advertising on car sales, 975
Efficiency studies, 693, 804, 952
Elasticity of demand, 729, 730, 732, 734, 735, 754
Electricity consumption, 290
E-mail services, 394
E-mail usage, 613
Employee education and income, 427
Energy conservation, 966, 974
Energy consumption and productivity, 654
Energy efficiency of appliances, 881
Establishing a trust fund, 1035
Expected auto sales, 465
Expected demand, 464
Expected home sales, 465
Expected product reliability, 464
Expected profit, 456, 464
Expected sales, 464
Expressway tollbooths, 1046
Factory workers’ wages, 505
Federal budget deficit, 596, 776
Federal debt, 620, 838
Female self-employed workforce, 833
Financial analysis, 213, 316
Financial planning, 305, 333
Financing a car, 301, 316, 317
Financing a college education, 989
Financing a home, 305, 316, 317, 318, 763, 765
Fisheries, 693, 697
Flex-time, 440

Forecasting commodity prices, 763
Forecasting profits, 763, 805
Forecasting sales, 682, 930
Foreign exchange, 131
401(k) retirement plans, 131, 405, 838
Franchises, 989, 1012
Fuel consumption of domestic cars, 1024
Fuel economy of cars, 696, 772
Gasoline consumption, 541
Gasoline prices, 815
Gasoline sales, 114, 118, 120, 121, 165, 815, 1045
Gasoline self-service sales, 585
Gender gap, 588
Google’s revenue, 806
Gross domestic product, 351, 674, 741, 763, 800, 820,
835
Growth in health club memberships, 713
Growth of bank deposits, 584
Growth of HMOs, 605, 697, 808, 1004
Growth of managed services, 785
Growth of service industries, 1026
Growth of Web sites, 860
Health-care costs, 694, 921
Health-care plan options, 358
Health club membership, 682, 713, 756
Home affordability, 312, 475
Home equity, 310
Home mortgages, 310, 316, 333, 1054, 1059, 1060
Home prices, 835, 961
Home refinancing, 317

(continued)


List of Applications (continued)
Home sales, 697
Home shopping industry, 659
Hotel chain growth, 972
Hotel occupancy rate, 603, 614, 718
Households with microwaves, 903
Housing appreciation, 290
Housing loans, 427
Housing starts, 604, 719, 749
Illegal ivory trade, 613
Income distributions, 431, 987, 996
Incomes of American families, 873, 884
Income streams, 981, 982, 1012, 1033, 1035
Indian gaming industry, 618
Industrial accidents, 472, 506
Inflation, 291, 739
In-flight service, 405
Information security software sales, 59
Input–output analysis, 153, 155, 157, 158, 159, 161
Installment contract sales, 995
Installment loans, 304, 333
Insurance claims, 117
Insurance probabilities, 435, 464
Inventory control and planning, 109, 116, 464, 653,
845, 846, 849, 854
Investment analysis, 275, 275, 302, 305, 317, 352,

464, 465, 474, 475, 983, 989
Investment clubs, 78, 79, 92, 93, 147
Investment in technology, 405
Investment options, 288, 291, 350, 355, 367
Investment planning, 78, 92, 196, 290
Investment portfolios, 116
Investment returns, 764
Investments, 78, 92, 105, 130, 271, 290, 352, 376
IRAs, 288, 302, 317, 984, 989
Keogh accounts, 764, 995
Land prices, 1071, 1084, 1110
LCDs versus CRTs, 50
Leasing, 49, 53
Life insurance premiums, 464
Life span of color television tubes, 1046
Life span of light bulbs, 1038, 1041
Linear depreciation, 31, 36, 68, 589
Loan amortization, 316, 319, 884, 1054
Loan delinquencies, 506
Loans at Japanese banks, 881
Locating a TV relay station, 1082
Lorentz curves, 985, 986, 989, 1012
Machine scheduling, 165
Magazine circulation, 917
Management decisions, 79, 93, 104, 364, 370, 805,
983
Manufacturing capacity, 595, 697, 790, 808, 831
Marginal average cost function, 724, 725, 733, 734
Marginal cost function, 723, 733, 734, 952, 994, 995
Marginal productivity of labor and capital, 1066

Marginal productivity of money, 1094
Marginal profit, 727, 733, 734, 951, 952
Marginal propensity to consume, 734
Marginal propensity to save, 734
Marginal revenue, 727, 733, 734, 881, 994
Market equilibrium, 46, 47, 48, 50, 53, 69, 615, 681,
682, 980
Market for cholesterol-reducing drugs, 57
Market research, 196
Market share, 117, 518, 521, 532, 672, 918
Marketing surveys, 347
Markup on a car, 573
Maximizing crop yield, 848
Maximizing oil production, 882
Maximizing production, 184, 1096
Maximizing profit, 45, 176, 183, 184, 187, 194, 229,
232, 235, 275, 827, 833, 834, 852, 853, 1081, 1091,
1093, 1095
Maximizing revenue, 834, 835, 848, 881

Maximizing sales, 1096
Meeting profit goals, 573
Metal fabrication, 846
Minimizing average cost, 829, 834, 853
Minimizing construction costs, 846, 853, 1095, 1096
Minimizing container costs, 843, 853, 847, 1096
Minimizing costs of laying cable, 848
Minimizing heating and cooling costs, 1085
Minimizing mining costs, 181, 195, 275
Minimizing packaging costs, 847, 853

Minimizing production costs, 834
Minimizing shipping costs, 8, 182, 183, 195, 253, 254,
272
Money market mutual funds, 291
Money market rates, 450
Morning traffic rush, 791
Mortgages, 310, 316, 317, 318, 333, 1010
Motorcycle sales, 117
Movie attendance, 383, 393
Multimedia sales, 744, 809
Municipal bonds, 290
Mutual funds, 290, 333
Net investment flow, 962
Net-connected computers in Europe, 60
New construction jobs, 708
Newsmagazine shows, 932
Newspaper subscriptions, 352
Nielsen television polls, 658, 672
Nuclear plant utilization, 21
Nurses’ salaries, 60
Office rents, 835
Oil production, 962, 974, 995, 1001
Oil production shortfall, 974
Oil spills, 682, 718, 754, 932, 1020, 1049
Online banking, 60, 880, 904
Online buyers, 692, 891
Online hotel reservations, 852
Online sales, 61, 291, 921
Online shopping, 61, 621
Online travel, 66

Operating costs of a truck, 759
Operating rates of factories, mines, and utilities, 831
Optimal charter flight fare, 848
Optimal market price, 878
Optimal selling price, 849
Optimal selling time, 882
Optimal speed of a truck, 849
Optimal subway fare, 842
Optimizing production schedules, 194, 234, 236, 271
Optimizing profit, 211, 232
Organizing business data, 109, 111
Organizing production data, 109, 111, 132
Organizing sales data, 108, 120
Outpatient service companies, 922
Outsourcing of jobs, 612, 717, 805
Packaging, 470, 499, 579, 616, 841, 843, 846, 853,
1084, 1085
PC shipments, 805
Pensions, 290, 291
Perpetual net income stream, 1035
Perpetuities, 1032, 1033, 1035, 1049
Personal consumption expenditure, 734
Personnel selection, 371, 412, 436
Petroleum consumption, 1023
Petroleum production, 165
Plans to keep cars, 405
Pocket computers, 952
Portable phone services, 692
Predicting sales figures, 16
Predicting the value of art, 16

Prefab housing, 183, 235
Present value of a franchise, 996, 1004
Present value of an income stream, 883, 984, 1033
Price of perfume, 881

Price of replacement automobile parts, 614
Price of wine, 882
Pricing, 147, 568
Prime interest rate, 654
Probability of engine failure, 489
Producers’ surplus, 978, 980, 988, 995, 1011, 1025,
1049
Product design, 847
Product reliability, 426, 428, 476, 505, 1046
Product safety, 392
Production costs, 732, 947
Production function, 1059
Production of steam coal, 1003
Production planning, 113, 126, 132, 133, 229, 235,
238, 254, 267
Production scheduling, 75, 89, 93, 176, 181, 182, 194,
210, 234, 235, 271, 272
Productivity fueled by oil, 882
Productivity of a country, 1071
Profit from sale of pagers, 603
Profit from sale of PDAs, 603
Profit functions, 33, 36, 68, 200
Profit of a vineyard, 616, 845
Projected retirement funds, 786
Projection TV sales, 994

Promissory notes, 290
Purchasing power, 291
Quality control, 370, 371, 376, 386, 393, 395, 399,
409, 412, 420, 421, 424, 427, 428, 430, 434, 435,
439, 440, 477, 485, 486, 489, 503, 506, 509, 573,
920
Racetrack design, 849
Rate comparisons, 290
Rate of bank failures, 744, 790, 838
Rate of change of cost functions, 722
Rate of change of DVD sales, 700
Rate of change of housing starts, 749
Rate of net investment, 1004
Rate of return on an investment, 290, 332
Real estate, 78, 92, 131, 287, 291, 942, 961, 1024
Real estate transactions, 131, 403, 463, 465
Recycling, 375
Refinancing a home, 317, 318
Reliability of a home theater system, 428
Reliability of computer chips, 901
Reliability of microprocessors, 1046
Reliability of robots, 1046
Reliability of security systems, 428
Resale value, 901
Retirement planning, 290, 304, 315, 317, 333, 995
Revenue growth of a home theater business, 291
Revenue of a charter yacht, 848
Revenue projection, 465
Reverse annuity mortgage, 989
Robot reliability, 489

Royalty income, 303
Salary comparisons, 329, 330
Sales forecasts, 579
Sales growth, 23, 329
Sales of camera phones, 852
Sales of digital signal processors, 619, 693
Sales of digital TVs, 612
Sales of drugs, 60, 66
Sales of DVD players vs. VCRs, 614
Sales of functional food products, 786
Sales of GPS equipment, 22, 60
Sales of loudspeakers, 994
Sales of mobile processors, 805
Sales of navigation systems, 22
Sales of prerecorded music, 588
Sales of security products, 703
Sales of vehicles, 476
Sales projections, 488
Sales promotions, 881


List of Applications (continued)
Sales tax, 36, 589
Sampling, 376, 409
Satellite radio subscriptions, 920
Selling price of DVD recorders, 612, 717
Service-utilization studies, 395
Shadow prices, 205
Shoplifting, 395
Shopping habits, 1045

Shuttle bus usage, 387
Sickouts, 838
Sinking fund, 313, 316, 333, 985
Social Security beneficiaries, 660
Social Security benefits, 36
Social Security contributions, 21
Social Security wage base, 61
Solvency of the Social Security system, 823
Spam messages, 602
Spending on fiber-optic links, 786
Spending on Medicare, 693
Staffing, 359
Starbucks’ annual sales, 66
Starbucks’ store count, 59, 66
Starting salaries, 476
Stock purchase, 570
Stock transactions, 122, 128, 165
Substitute commodities, 1067, 1072
Sum-of-the-years’-digits method of depreciation, 329
Supply and demand, 35, 37, 38, 48, 50, 69, 608, 609,
615, 692, 750, 763, 932
Switching jobs, 405
Tax planning, 302, 303, 305, 317, 333
Tax-deferred annuity, 302
Taxicab movement, 517, 529
Telemarketing, 506
Television commercials, 235
Television pilots, 450
Television programming, 370
Testing new products, 384, 391, 392, 741

Theater bookings, 506
Ticket revenue, 147
Time on the market, 809, 838
Tour revenue, 145
Tracking with GPS, 860
Transportation, 181, 210, 253
Transportation problem, 178, 195
Tread lives of tires, 1026
Trust funds, 279, 290, 316, 330, 1035
TV households, 403
TV-viewing patterns, 672, 717, 932
Unemployment rates, 464
Union bargaining issues, 358
U.S. daily oil consumption, 1025
U.S. drug sales, 60
U.S. financial transactions, 50
U.S. nutritional supplements market, 613
U.S. online banking households, 60
U.S. strategic petroleum reserves, 1025
Use of automated office equipment, 541
Use of diesel engines, 838
Value of an investment, 602
VCR ownership, 1011
Venture-capital investment, 835
Violations of the building code, 488
Volkswagen’s revenue, 475
Wages, 466, 669
Waiting lines, 370, 446, 450, 454, 466, 1045
Warehouse problem, 179, 183, 249
Warranties, 358, 400, 505

Waste generation, 66
Web hosting, 786
Wilson lot-size formula, 1060
Wireless subscribers, 61
Worker efficiency, 590, 611, 693, 804, 820, 853
World production of coal, 961, 995, 1003

Worldwide production of vehicles, 721
Yahoo! in Europe, 891
Zero coupon bonds, 290, 291

SOCIAL SCIENCES
Accident prevention, 392
Age distribution in a town, 479
Age distribution of renters, 436
Age of drivers in crash fatalities, 787
Aging drivers, 612
Aging population, 717, 742
Air pollution, 718, 786, 787, 791, 806, 834, 922, 930,
1025
Air purification, 741, 953, 974
Alcohol-related traffic accidents, 1003
Americans without health insurance, 476
Annual college costs, 66
Arrival times, 394
Arson for profit, 1059
Auto-accident rates, 435, 464
Automobile pollution, 600
Bursts of knowledge, 648
Car theft, 427

Civil service exams, 505
Closing the gender gap in education, 589
College admissions, 22, 59, 69, 131, 427, 440, 500
College graduates, 489
College majors, 436, 521
Committee selection, 366
Commuter options, 357
Commuter trends, 350, 520, 530, 994
Commuting times, 461
Compliance with seat belt laws, 435
Computer security, 809
Conservation of oil, 970
Consumer decisions, 8, 289, 329
Consumer surveys, 347, 349, 350, 351, 404
Continuing education enrollment, 718
Correctional supervision, 395
Cost of removing toxic waste, 638, 702, 705, 820
Course enrollments, 404
Court judgment, 289
Crime, 350, 435, 741, 763, 781, 835
Cube rule, 590
Curbing population growth, 694
Decline of union membership, 595
Demographics, 902
Dependency ratio, 806
Disability benefits, 741
Disability rates, 860
Disposition of criminal cases, 396
Dissemination of information, 902
Distribution of families by size, 450

Distribution of incomes, 573, 987, 989
Drivers’ tests, 371, 413
Driving age requirements, 474
Education, 505, 541
Educational level of mothers and daughters, 523
Educational level of senior citizens, 18
Educational level of voters, 426
Education and income, 427
Effect of budget cuts on crime rates, 804
Effect of smoking bans, 804
Elderly workforce, 786
Elections, 376, 435
Election turnout, 476
Endowments, 1033, 1035
Energy conservation, 966, 970
Energy needs, 949
Enrollment planning, 436, 521
Exam scores, 358, 371, 450, 466, 475, 489
Female life expectancy, 716, 932
Financing a college education, 290, 317
Food stamp recipients, 839

Foreign-born residents, 835
Gender gap, 588, 589
Global epidemic, 954
Global supply of plutonium, 603
Grade distributions, 393, 505
Growth of HMOs, 697, 808
Gun-control laws, 406
Health-care spending, 694, 697, 921

Highway speeds, 505
HMOs, 605
Homebuying trends, 531
Homeowners’ choice of energy, 521, 531
Hours worked in some countries, 475
Immigration, 614, 900
Income distributions, 987
Increase in juvenile offenders, 885
Intervals between phone calls, 1046
Investment portfolios, 122
IQs, 505
Jury selection, 370
Lay teachers at Roman Catholic schools, 902, 905
Learning curves, 648, 653, 705, 763, 897, 901, 932
Library usage, 448
Life expectancy, 117
Logistic curves, 899
Male life expectancy at 60, 769
Marijuana arrests, 621, 954
Marital status of men, 475
Marital status of women, 509
Married households, 860
Mass transit, 842
Mass-transit subsidies, 59
Medical school applicants, 786
Membership in credit unions, 962
Mortality rates, 117
Narrowing gender gap, 22
Network news viewership, 531
Oil used to fuel productivity, 882

One- and two-income families, 531
Opinion polls, 358, 393, 435, 437
Organizing educational data, 131, 344
Organizing sociological data, 450, 474, 475
Overcrowding of prisons, 603, 787
Ozone pollution, 922
Percentage of females in the labor force, 885
Percentage of population relocating, 880
Political polls, 358, 387, 396, 520
Politics, 344, 432, 434, 590
Population density, 1105, 1106, 1107, 1109
Population growth, 329, 638, 642, 682, 694, 706, 708,
922, 932, 954, 975, 996
Population growth in Clark County, 620, 806, 946
Population growth in the 21st century, 902, 905
Population over 65 with high-school diplomas, 18
Prison population, 603, 787
Professional women, 531
Psychology experiments, 357, 520, 530
Public housing, 413
Quality of environment, 785, 853
Recycling programs, 1011
Registered vehicles in Massachusetts, 590
Research funding, 147
Restaurant violations of the health code, 488
Ridership, 78, 92
Rising median age, 590
Risk of an airplane crash, 406
Rollover deaths, 405
Safe drivers, 596

Same-sex marriage, 394
SAT scores, 59, 351, 398
Seat-belt compliance, 435
Selection of Senate committees, 371
Selection of Supreme Court judges, 436
Senior citizens, 953

(continued)


List of Applications (continued)
Senior workforce, 833, 853
Single female-headed households with children, 952
Small-town revival, 520
Social ladder, 436
Socially responsible funds, 717
Social programs planning, 182, 195
Solar energy, 485, 521
Solar power, 612
Spending on medical devices, 612
Spread of rumor, 803
Student dropout rate, 351
Student enrollment, 426, 932
Student financial aid, 427
Student loans, 316
Student reading habits, 351
Student surveys, 351, 376
Study groups, 370
Switching Internet service providers (ISPs), 428
Teacher attitudes, 404

Teaching assistantships, 370
Television-viewing polls, 358, 450
Thurstone learning models, 682, 718
Time intervals between phone calls, 1046
Tracking with GPS, 860
Traffic studies, 394, 694, 718
Traffic-flow analysis, 101, 105
Transcription of court proceedings, 540
Trends in auto ownership, 532, 568
TV viewing patterns, 658, 717, 932
UN Security Council voting, 368, 370
Urban–suburban population flow, 515, 516, 521
U.S. birth rate, 474
U.S. Census, 995
U.S. nursing shortage, 787
U.S. population by age, 450
U.S. population growth, 791
U.S. senior citizens, 962
Use of public transportation, 78, 92
Voter affiliation, 131
Voter registration, 1011
Voters, 488
Voter turnout, 437
Voting patterns, 435
Voting quorums, 372
Waiting times, 1045
Waste disposal, 963
Women in the professions, 531
Working mothers, 717, 742
Working-age population, 614

World energy consumption, 66
World population growth, 791, 835, 880, 884, 900

LIFE SCIENCES
Absorption of drugs, 861, 863, 872, 882, 883, 903,
905, 908, 965
Absorption of light, 892
Administration of an IV solution, 654
Adult obesity, 768
Aids in Massachusetts, 965
Amount of rainfall, 642, 923
Animal nutrition, 196, 271
Anticipated rise in Alzheimer’s patients, 590, 594, 743
Arteriosclerosis, 714, 718
Average weights and heights of infants, 671, 932
Bacteria growth, 330
Birth weights of infants, 499
Birthrate of endangered species, 602
Birthrates, 474
Blood alcohol level, 881, 882
Blood flow in an artery, 922, 953
Blood pressure, 871
Blood types, 386, 393, 394, 489
Body mass, 1058

Cancer survivors, 590
Carbon-14 dating, 896, 901
Carbon monoxide in the air, 697, 717, 896, 901, 922
Cardiac output, 1013, 1019
Chemical reactions, 902

Child obesity, 693
Cholesterol levels, 116
Clark’s rule, 68, 681
Color blindness, 416
Concentration of a drug in an organ, 933
Concentration of a drug in the bloodstream, 638, 705,
786, 820, 882, 960, 963, 1003
Concentration of glucose in the bloodstream, 903
Conservation of species, 688, 694, 740
Contraction of the trachea during a cough, 828
Corrective lens use, 395
Cost of hospital care, 290
Cowling’s rule, 37
Cricket chirping and temperature, 37
Crop planning, 181, 195, 210, 235, 269, 271
Crop yield, 672, 761, 848, 885, 965
Dietary planning, 79, 93, 132, 147, 182, 195, 254, 272
Diet-mix problems, 147, 254
Diffusion, 1004
Doomsday situation, 638
Drug dosages, 37, 611, 705
Drug effectiveness, 509
Drug testing, 489, 506
Effect of bactericide, 672, 705
Effect of enzymes on chemical reactions, 820
Energy expended by a fish, 654, 836
Environment of forests, 785
Epidemic models, 882, 902, 908, 1010
Eradication of polio, 881
Extinction situation, 884

Female life expectancy at 60, 932
Fertilizer mixtures, 78, 92, 147
Flights of birds, 849
Flow of blood in an artery, 963, 922
Flu epidemic, 882, 908
Forensic science, 872
Forestry, 671, 785
Formaldehyde levels, 705
Friend’s rule, 589
Gastric bypass surgeries, 921
Genetically modified crops, 920
Genetics, 531, 538
Global epidemic, 954
Gompertz growth curve, 903
Groundfish population, 693, 697
Growth of a cancerous tumor, 588, 762
Growth of a fruit fly population, 630, 902, 905, 1011
Growth of bacteria, 674, 894, 900, 907
Harbor cleanup, 590
Heart transplant survival rate, 503
Heights of children, 891, 922
Heights of trees, 872
Heights of women, 479, 509
Ideal heights and weights for women, 22
Importance of time in treating heart attacks, 707
Index of environmental quality, 853
Length of a hospital stay, 1049
Lengths of fish, 872, 901, 905
Lengths of infants, 1026
Life span of a plant, 1045

Male life expectancy, 60, 65, 769
Measuring cardiac output, 1026
Medical diagnoses, 436
Medical records, 501
Medical research, 428, 435
Medical surveys, 423
Nuclear fallout, 901
Nutrition, 104, 147, 177, 188, 254

Obese children in the United States, 613
Obesity in America, 694, 741
Organizing medical data, 116
Outpatient visits, 61
Over-100 population, 880
Oxygen-restoration rate in a pond, 655, 702, 820, 834
Ozone pollution, 922
Photosynthesis, 639
Poiseuille’s law, 590, 1058
Polio immunization, 881
Preservation of species, 688
Prevalence of Alzheimer’s patients, 590, 594, 743, 785
Probability of transplant rejection, 428
Pulse rates, 718, 974
Radioactive decay, 895, 901, 903, 907
Rate of growth of a tumor, 905
Reaction of a frog to a drug, 613
Reaction to a drug, 836
Reliability of medical tests, 434, 435
Rising median age, 590
Senior citizens’ health care, 614

Serum cholesterol levels, 501
Smoking and emphysema, 423
Speed of a chemical reaction, 639
Spread of contagious disease, 853
Spread of flu epidemic, 819, 882, 899, 902, 908
Spread of HIV, 697
Storing radioactive waste, 848
Strain of vertebrae, 891
Success of heart transplants, 486
Surface area of a horse, 763
Surface area of a lake, 1049
Surface area of a single-celled organism, 588
Surface area of the human body, 922, 1059, 1072
Surgeries in physicians’ offices, 790, 809
Testosterone use, 612
Time rate of growth of a tumor, 905
Toxic pollutants, 638
Unclogging arteries, 762
U.S. infant mortality rate, 908
Velocity of blood, 692, 835
Veterinary science, 196, 271
Violations of the health code, 488
Von Bertanlanffy growth function, 902
Waiting times, 1045
Walking versus running, 613
Water pollution, 802
Weber–Fechner law, 892
Weight of whales, 22
Weights of children, 882
Weiss’s law, 654

Whale population, 688, 962
Yield of an apple orchard, 616

GENERAL INTEREST
Automobile options, 341
Automobile selection, 358
Ballast dropped from a balloon, 921
Birthday problem, 410, 414
Blackjack, 357, 413
Blowing soap bubbles, 755
Boston Marathon, 783
Boyle’s law, 590
Car pools, 370
Carrier landing, 923
Coast Guard patrol search mission, 755
Code words, 358
Coin tosses, 357, 509
Computer dating, 358
Computing phone bills, 132
Crossing the finish line, 923
Designing a grain silo, 848
Designing a Norman window, 616, 847


List of Applications (continued)
Engine efficiency, 1072
Error measurement, 760, 761, 762
Estimating the amount of paint required, 762
Estimating the flow rate of a river, 1025, 1026
Exercise program, 329

Expected snowfall, 1045
Family food expenditure, 290
Fencing, 615, 840, 846
Flight of a rocket, 694, 785, 804, 830, 833, 922
Flight path of a plane, 659
Frequency of road repairs, 1045
Gambler’s ruin, 536, 537
Game shows, 386
IQs, 1058
Keeping with the traffic flow, 595
Launching a fighter aircraft, 923
License plate numbers, 358
Lightning deaths, 395
Lotteries, 305, 358, 464, 989
Magnitude of earthquakes, 871, 892

Manned bomber research, 432
Menu selection, 358
Meteorology, 393
Motion of a maglev, 622, 738, 920
Newton’s law of cooling, 872, 904, 962
Parking fees, 654
Period of a communications satellite, 766
Poker, 366, 376, 413
Postal regulations, 590, 653, 847
Raffles, 406, 457
Reaction time of a motorist, 1045
Rings of Neptune, 760, 766
Rocket launch, 751
Roulette, 396, 413, 458, 459, 465

Safe drivers, 596
Saving for a college education, 291, 333
Slot machines, 359, 413
Sound intensity, 872
Speedboat racing, 952
Sports, 370, 372, 387, 466, 488, 506, 509

Stopping distance of a racing car, 693
Strength of a beam, 848
Surface area of the Central Park reservoir, 1025
Sweepstakes, 396
Team selection, 376
Temperature conversion, 21, 37
Terminal velocity, 819
Travel options, 356
Trial run of an attack submarine, 1024
Turbo-charged engine performance, 975
Vacation costs, 93
Velocity of a car, 673, 917, 919, 920, 962
Velocity of a dragster, 1003
VTOL aircraft, 741
Wardrobe selection, 357
Windchill factor, 1072
Women’s soccer, 806
Zodiac signs, 414


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College
Mathematics
for the Managerial, Life,
and Social Sciences
Seventh Edition

S. T. TAN
STONEHILL COLLEGE

Australia • Brazil • Canada • Mexico • Singapore • Spain
United Kingdom • United States


College Mathematics
for the Managerial, Life, and Social Sciences, 7e
S. T. Tan

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CONTENTS

TO PAT, BILL, AND MICHAEL

iii


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CONTENTS

v

Contents

Preface
CHAPTER 1

xiii

Straight Lines and Linear Functions
1.1
1.2
1.3
1.4
*1.5

CHAPTER 2

1

The Cartesian Coordinate System 2
Straight Lines 10
Using Technology: Graphing a Straight Line 24
Linear Functions and Mathematical Models 28
Using Technology: Evaluating a Function 39
Intersection of Straight Lines 42
Using Technology: Finding the Point(s) of Intersection of Two Graphs
The Method of Least Squares 54
Using Technology: Finding an Equation of a Least-Squares Line 63
Chapter 1 Summary of Principal Formulas and Terms 67

Chapter 1 Concept Review Questions 67
Chapter 1 Review Exercises 68
Chapter 1 Before Moving On 69

Systems of Linear Equations and Matrices
2.1
2.2
2.3

2.4
2.5
2.6
*2.7

52

71

Systems of Linear Equations: An Introduction 72
Systems of Linear Equations: Unique Solutions 80
Using Technology: Systems of Linear Equations: Unique Solutions 94
Systems of Linear Equations: Underdetermined and Overdetermined Systems
Using Technology: Systems of Linear Equations: Underdetermined and
Overdetermined Systems 106
Matrices 108
Using Technology: Matrix Operations 118
Multiplication of Matrices 121
Using Technology: Matrix Multiplication 134
The Inverse of a Square Matrix 136
Using Technology: Finding the Inverse of a Square Matrix 150

Leontief Input–Output Model 153
Using Technology: The Leontief Input–Output Model 160

97

Note: Sections marked with an asterisk are not prerequisites for later material.

v


vi

CONTENTS

Chapter 2 Summary of Principal Formulas and Terms 163
Chapter 2 Concept Review Questions 163
Chapter 2 Review Exercises 164
Chapter 2 Before Moving On 166

CHAPTER 3

Linear Programming: A Geometric Approach 167
3.1
3.2
3.3
*3.4

Graphing Systems of Linear Inequalities in Two Variables 168
Linear Programming Problems 176
Graphical Solution of Linear Programming Problems 185

Sensitivity Analysis 198
PORTFOLIO: Morgan Wilson 206

Chapter 3 Summary of Principal Terms 212
Chapter 3 Concept Review Questions 212
Chapter 3 Review Exercises 213
Chapter 3 Before Moving On 214

CHAPTER 4

Linear Programming: An Algebraic Approach
4.1
4.2
*4.3

CHAPTER 5

The Simplex Method: Standard Maximization Problems 216
Using Technology: The Simplex Method: Solving Maximization Problems 238
The Simplex Method: Standard Minimization Problems 243
Using Technology: The Simplex Method: Solving Minimization Problems 255
The Simplex Method: Nonstandard Problems 260
Chapter 4 Summary of Principal Terms 274
Chapter 4 Concept Review Questions 274
Chapter 4 Review Exercises 274
Chapter 4 Before Moving On 275

Mathematics of Finance
5.1

5.2
5.3

277

Compound Interest 278
Using Technology: Finding the Accumulated Amount of an Investment, the
Effective Rate of Interest, and the Present Value of an Investment 292
Annuities 296
Using Technology: Finding the Amount of an Annuity 306
Amortization and Sinking Funds 309
PORTFOLIO: Mark Weddington 313

*5.4

215

Using Technology: Amortizing a Loan 319
Arithmetic and Geometric Progressions 322
Chapter 5 Summary of Principal Formulas and Terms 331
Chapter 5 Concept Review Questions 331
Chapter 5 Review Exercises 332
Chapter 5 Before Moving On 334


CONTENTS

CHAPTER 6

Sets and Counting

335

6.1
6.2
6.3

Sets and Set Operations 336
The Number of Elements in a Finite Set
The Multiplication Principle 353

6.4

Permutations and Combinations 359
Using Technology: Evaluating n!, P(n, r), and C(n, r) 373
Chapter 6 Summary of Principal Formulas and Terms 374
Chapter 6 Concept Review Questions 375
Chapter 6 Review Exercises 375
Chapter 6 Before Moving On 377

346

PORTFOLIO: Stephanie Molina 356

CHAPTER 7

Probability

379

7.1
7.2
7.3

Experiments, Sample Spaces, and Events
Definition of Probability 388
Rules of Probability 397

380

7.4
7.5
7.6

Use of Counting Techniques in Probability 407
Conditional Probability and Independent Events 414
Bayes’ Theorem 429
Chapter 7 Summary of Principal Formulas and Terms 438
Chapter 7 Concept Review Questions 439
Chapter 7 Review Exercises 439
Chapter 7 Before Moving On 441

PORTFOLIO: Todd Good 401

CHAPTER 8

Probability Distributions and Statistics
8.1
8.2

Distributions of Random Variables 444
Using Technology: Graphing a Histogram
Expected Value 454

443

451

PORTFOLIO: Ann-Marie Martz 461

8.3
8.4
8.5
8.6

Variance and Standard Deviation 467
Using Technology: Finding the Mean and Standard Deviation
The Binomial Distribution 480
The Normal Distribution 490
Applications of the Normal Distribution 499
Chapter 8 Summary of Principal Formulas and Terms 507
Chapter 8 Concept Review Questions 508
Chapter 8 Review Exercises 508
Chapter 8 Before Moving On 509

478

vii

viii

CONTENTS

CHAPTER 9

Markov Chains
9.1
9.2
9.3

CHAPTER 10

511

Markov Chains 512
Using Technology: Finding Distribution Vectors 522
Regular Markov Chains 523
Using Technology: Finding the Long-Term Distribution Vector
Absorbing Markov Chains 535
Chapter 9 Summary of Principal Formulas and Terms 543
Chapter 9 Concept Review Questions 543
Chapter 9 Review Exercises 544
Chapter 9 Before Moving On 545

Precalculus Review
10.1
10.2
10.3
10.4

CHAPTER 11

547

Exponents and Radicals 548
Algebraic Expressions 552
Algebraic Fractions 560
Inequalities and Absolute Value 568
Chapter 10 Summary of Principal Formulas and Terms 574
Chapter 10 Review Exercises 574

Functions, Limits, and the Derivative
11.1
11.2
11.3
11.4
11.5
11.6

CHAPTER 12

533

577

Functions and Their Graphs 578
Using Technology: Graphing a Function 592
The Algebra of Functions 596
Functions and Mathematical Models 604

Using Technology: Finding the Points of Intersection of Two Graphs and Modeling
Limits 621
Using Technology: Finding the Limit of a Function 640
One-Sided Limits and Continuity 643
Using Technology: Finding the Points of Discontinuity of a Function 656
The Derivative 659
Using Technology: Graphing a Function and Its Tangent Line 676
Chapter 11 Summary of Principal Formulas and Terms 679
Chapter 11 Concept Review Questions 679
Chapter 11 Review Exercises 680
Chapter 11 Before Moving On 682

Differentiation 683
12.1
12.2

Basic Rules of Differentiation 684
Using Technology: Finding the Rate of Change of a Function
The Product and Quotient Rules 698
Using Technology: The Product and Quotient Rules 707

695

617


CONTENTS

12.3
12.4

12.5

The Chain Rule 709
Using Technology: Finding the Derivative of a Composite Function
Marginal Functions in Economics 721
Higher-Order Derivatives 736

720

PORTFOLIO: Steve Regenstreif 737

*12.6
12.7

CHAPTER 13

Using Technology: Finding the Second Derivative of a Function at a Given
Point 743
Implicit Differentiation and Related Rates 745
Differentials 756
Using Technology: Finding the Differential of a Function 764
Chapter 12 Summary of Principal Formulas and Terms 766
Chapter 12 Concept Review Questions 767
Chapter 12 Review Exercises 767
Chapter 12 Before Moving On 769

Applications of the Derivative
13.1
13.2
13.3

13.4
13.5

CHAPTER 14

771

Applications of the First Derivative 772
Using Technology: Using the First Derivative to Analyze a Function 788
Applications of the Second Derivative 791
Using Technology: Finding the Inflection Points of a Function 807
Curve Sketching 809
Using Technology: Analyzing the Properties of a Function 822
Optimization I 824
Using Technology: Finding the Absolute Extrema of a Function 837
Optimization II 839
Chapter 13 Summary of Principal Terms 851
Chapter 13 Concept Review Questions 851
Chapter 13 Review Exercises 852
Chapter 13 Before Moving On 854

Exponential and Logarithmic Functions
14.1
14.2
14.3

Exponential Functions 856
Using Technology 862
Logarithmic Functions 863
Differentiation of Exponential Functions

855

873

PORTFOLIO: Robert Derbenti 874

14.4
*14.5

Using Technology 884
Differentiation of Logarithmic Functions 885
Exponential Functions as Mathematical Models 893
Using Technology: Analyzing Mathematical Models 903
Chapter 14 Summary of Principal Formulas and Terms 906
Chapter 14 Concept Review Questions 906
Chapter 14 Review Exercises 907
Chapter 14 Before Moving On 908

ix


x

CONTENTS

CHAPTER 15

Integration
15.1

15.2
15.3
15.4
15.5

15.6
*15.7

CHAPTER 16

909

Antiderivatives and the Rules of Integration 910
Integration by Substitution 924
Area and the Definite Integral 934
The Fundamental Theorem of Calculus 943
Using Technology: Evaluating Definite Integrals 954
Evaluating Definite Integrals 955
Using Technology: Evaluating Definite Integrals for Piecewise-Defined
Functions 964
Area between Two Curves 966
Using Technology: Finding the Area between Two Curves 977
Applications of the Definite Integral to Business and Economics 978
Using Technology: Business and Economic Applications 990
Chapter 15 Summary of Principal Formulas and Terms 991
Chapter 15 Concept Review Questions 993
Chapter 15 Review Exercises 993
Chapter 15 Before Moving On 996

Additional Topics in Integration

16.1
*16.2
*16.3
16.4
*16.5

997

Integration by Parts 998
Integration Using Tables of Integrals 1005
Numerical Integration 1012
Improper Integrals 1027
Applications of Calculus to Probability 1036
PORTFOLIO: Gary Li 1043

Chapter 16 Summary of Principal Formulas and Terms 1047
Chapter 16 Concept Review Questions 1048
Chapter 16 Review Exercises 1048
Chapter 16 Before Moving On 1050

CHAPTER 17

Calculus of Several Variables
17.1
17.2
17.3

1051

Functions of Several Variables 1052

Partial Derivatives 1061
Using Technology: Finding Partial Derivatives at a Given Point
Maxima and Minima of Functions of Several Variables 1075

1074

PORTFOLIO: Kirk Hoiberg 1078

17.4
17.5

Constrained Maxima and Minima and the Method of Lagrange Multipliers
Double Integrals 1097
Chapter 17 Summary of Principal Terms 1111
Chapter 17 Concept Review Questions 1111
Chapter 17 Review Exercises 1112
Chapter 17 Before Moving On 1114

1086


CONTENTS

APPENDIX A

The System of Real Numbers

APPENDIX B

Tables

1118

Table 1: Binomial Probabilities 1119
Table 2: The Standard Normal Distribution

1123

Answers to Odd-Numbered Exercises
Index

1115

1191

1125

xi


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Preface

M

ath is an integral part of our daily life. College Mathematics for the Managerial, Life, and Social Sciences, Seventh Edition, covers the standard topics in mathematics and calculus that are usually covered in a two-semester course for students in
the managerial, life, and social sciences. The only prerequisite for understanding this
book is a year of high school algebra. Our objective for this Seventh Edition is twofold: (1) to write an applied text that motivates students and (2) to make the book a

useful tool for instructors. We hope that with this present edition we have come closer
to realizing our goal.

General Approach
■

Coverage of Topics Since the book contains more than enough material for
the usual two-semester or three-quarter course, the instructor may be flexible in
choosing the topics most suitable for his or her course. The following chart on
chapter dependency is provided to help the instructor design a course that is most
suitable for the intended audience.

1

5

6

10

Straight Lines and
Linear Functions

Mathematics
of Finance

Sets and Counting

Precalculus
Review

2

7

11

Systems of Linear
Equations and Matrices

Probability

Functions, Limits
and the Derivative

3
Linear Programming:
A Geometric Approach

4
Linear Programming:
An Algebraic Approach

8

12

Probability Distributions
and Statistics

Differentiation

9

13

Markov Chains

Applications
of the Derivative

17

14

Calculus of Several
Variables

Exponential and
Logarithmic Functions

16

15

Additional Topics
in Integration

Integration

xiii


xiv

■

PREFACE

■

Custom Publishing Due to the flexible nature of the topic coverage, instructors
can easily design a custom text containing only those topics that are most suitable
for their course. Please see your sales representative for more information on
Brooks/Cole’s custom publishing options.

■

Level of Presentation Our approach is intuitive, and we state the results informally. However, we have taken special care to ensure that this approach does not
compromise the mathematical content and accuracy.

Approach A problem-solving
approach is stressed throughout
the book. Numerous examples
and applications are used to
illustrate each new concept and
result in order to help the students comprehend the material
presented. An emphasis is
placed on helping the students
formulate, solve, and interpret

the results of the problems
involving applications. Very
early on in the text, students are
given practice in setting up word
problems (Section 1.3) and
developing modeling skills.
Later when the topic of linear
programming is introduced, one
entire section is devoted to modeling and setting up the problems (Section 3.2). Also, in
calculus, guidelines are given
for constructing mathematical
models (Section 11.3). As another example, when optimization problems are covered the
problems are presented in two
sections. First students are asked
to solve optimization problems
in which the objective function
to be optimized is given (Section 13.4) and then students are
asked to solve problems where
they have to formulate the optimization problems to be solved
(Section 13.5).

A Maximization Problem
As an example of a linear programming problem in which the objective function is
to be maximized, let’s consider the following simplified version of a production
problem involving two variables.
APPLIED EXAMPLE 1 A Production Problem Ace Novelty wishes to
produce two types of souvenirs: type A and type B. Each type-A souvenir
will result in a profit of $1, and each type-B souvenir will result in a profit of
$1.20. To manufacture a type-A souvenir requires 2 minutes on machine I and
1 minute on machine II. A type-B souvenir requires 1 minute on machine I and

3 minutes on machine II. There are 3 hours available on machine I and 5 hours
available on machine II for processing the order. How many souvenirs of each
type should Ace make in order to maximize its profit?
As a first step toward the mathematical formulation of this problem,
we tabulate the given information, as shown in Table 1.

Solution

TABLE 1
Type A

Type B

Time Available

Machine II

2 min
1 min

1 min
3 min

180 min
300 min

Profit/Unit

$1

$1.20

Machine I

Let x be the number of type-A souvenirs and y be the number of type-B souvenirs
to be made. Then, the total profit P (in dollars) is given by
P ϭ x ϩ 1.2y

Guidelines for Constructing Mathematical Models
1. Assign a letter to each variable mentioned in the problem. If appropriate,
draw and label a figure.
2. Find an expression for the quantity sought.
3. Use the conditions given in the problem to write the quantity sought as a
function f of one variable. Note any restrictions to be placed on the domain
of f from physical considerations of the problem.

APPLIED EXAMPLE 4 Enclosing an Area The owner of the Rancho
Los Feliz has 3000 yards of fencing with which to enclose a rectangular piece
of grazing land along the straight portion of a river. Fencing is not required along
the river. Letting x denote the width of the rectangle, find a function f in the variable x giving the area of the grazing land if she uses all of the fencing (Figure 57).
Solution

1. This information was given.

x

y

2. The area of the rectangular grazing land is A ϭ xy. Next, observe that the
amount of fencing is 2x ϩ y and this must be equal to 3000 since all the fencing is used; that is,

2x ϩ y ϭ 3000

x

3. From the equation we see that y ϭ 3000 Ϫ 2x. Substituting this value of y into
the expression for A gives
A ϭ xy ϭ x(3000 Ϫ 2x) ϭ 3000x Ϫ 2x 2

FIGURE 20
The rectangular grazing land has width
x and length y.

Finally, observe that both x and y must be nonnegative since they represent the
width and length of a rectangle, respectively. Thus, x Ն 0 and y Ն 0. But the
latter is equivalent to 3000 Ϫ 2x Ն 0, or x Յ 1500. So the required function is
f (x) ϭ 3000x Ϫ 2x 2 with domain 0 Յ x Յ 1500.


PREFACE

Intuitive Introduction to
Concepts Mathematical concepts are introduced with concrete real-life examples, wherever appropriate. Our goal here
is to capture students’ interest
and show the relevance of mathematics to their everyday life.
For example, curve-sketching
(Section 13.3) is introduced in
the manner shown here.

Consider, for example, the graph of the function giving the Dow-Jones
Industrial Average (DJIA) on Black Monday, October 19, 1987 (Figure 47). Here,

t ϭ 0 corresponds to 8:30 a.m., when the market was open for business, and t ϭ 7.5
corresponds to 4 p.m., the closing time. The following information may be gleaned
from studying the graph.
y
2200

(2, 2150)

2100

DJIA

■

xv

(1, 2047)

2000

(4, 2006)
1900
1800
1700

FIGURE 45
The Dow-Jones Industrial Average on
Black Monday

0

1

2

3

4
Hours

5

6

7

8

t

Source: Wall Street Journal

The graph is decreasing rapidly from t ϭ 0 to t ϭ 1, reflecting the sharp drop
in the index in the first hour of trading. The point (1, 2047) is a relative minimum
point of the function, and this turning point coincides with the start of an aborted
recovery. The short-lived rally, represented by the portion of the graph that is
increasing on the interval (1, 2), quickly fizzled out at t ϭ 2 (10:30 a.m.). The relative maximum point (2, 2150) marks the highest point of the recovery. The function
is decreasing in the rest of the interval. The point (4, 2006) is an inflection point of
the function; it shows that there was a temporary respite at t ϭ 4 (12:30 p.m.).
However, selling pressure continued unabated, and the DJIA continued to fall until

the closing bell. Finally, the graph also shows that the index opened at the high of
the day [ f (0) ϭ 2247 is the absolute maximum of the function] and closed at the low
of the day [ f Ĩᎏ125ᎏƠ ϭ 1739 is the absolute minimum of the function], a drop of 508
points!*

Motivation
Illustrating the practical value of mathematics in applied areas is an important objective of our approach. What follows are examples of how we have implemented this
relevant approach throughout the text.
■

Real-life Applications Current
and relevant examples and exercises are drawn from the fields
of business, economics, social
and behavioral sciences, life sciences, physical sciences, and
other fields of interest. In the
examples, these are highlighted
with new icons that illustrate the
various applications.

APPLIED EXAMPLE 4 Financing a Car After making a down payment
of $4000 for an automobile, Murphy paid $400 per month for 36 months with
interest charged at 12% per year compounded monthly on the unpaid balance.
What was the original cost of the car? What portion of Murphys total car payments went toward interest charges?
Solution

The loan taken up by Murphy is given by the present value of the

annuity
400[1 Ϫ (1.01)Ϫ36]
––

P ϭ ᎏᎏ ϭ 400a 36
Խ0.01
0.01


xvi

■

■

PREFACE

Developing Modeling Skills We believe that one of the most
important skills a student can acquire is the ability to translate a
real problem into a model that can provide insight into the problem.
Many of the applications are based on mathematical models (functions) that the author has constructed using data drawn from various
sources, including current newspapers, magazines, and data obtained
through the Internet. Sources are given in the text for these applied
problems. In Sections 1.3 and 11.3, the modeling process is discussed
and students are asked to use models (functions) constructed from
real-life data to answer questions about the Market for CholesterolReducing Drugs, HMO Membership, and the Driving Costs for a
Ford Taurus.
Connections One example (the
maglev example) is used as a
common thread throughout the
development of calculus—from
limits through integration. The
goal here is to show students the
connection between the concepts

presented—limits, continuity,
rates of change, the derivative,
the definite integral, and so on.

FIGURE 22
A maglev moving along an elevated
monorail track

15. BLACKBERRY SUBSCRIBERS According to a study conducted in
2004, the number of subscribers of BlackBerry, the handheld
e-mail devices manufactured by Research in Motion Ltd.,
is expected to be
N(t)

0.0675t 4

0.5083t 3
(0 t

0.893t 2
4)

0.66t

0.32

where N(t) is measured in millions and t in years, with
t 0 corresponding to the beginning of 2002.
a. How many BlackBerry subscribers were there at the
beginning of 2002?

b. What is the projected number of BlackBerry subscribers
at the beginning of 2006?
Source: ThinkEquity Partners

t=0

t=1

t=2

t=3

t = 10

0

4

16

36

400

s (feet)

Suppose we want to find the velocity of the maglev at t ϭ 2. This is just the
velocity of the maglev as shown on its speedometer at that precise instant of time.
Offhand, calculating this quantity using only Equation (1) appears to be an impossible task; but consider what quantities we can compute using this relationship.
Obviously, we can compute the position of the maglev at any time t as we did earlier for some selected values of t. Using these values, we can then compute the average velocity of the maglev over an interval of time. For example, the average velocity of the train over the time interval [2, 4] is given by

Utilizing Tools Students Use
■

■

Exploring with Technology
Questions Here technology is
used to explore mathematical
concepts and to shed further
light on examples in the text.
These optional questions appear
throughout the main body of the
text and serve to enhance the student’s understanding of the concepts and theory presented. Often
the solution of an example in the
text is augmented with a graphical or numerical solution. Complete solutions to these exercises
are given in the Instructor’s
Solution Manual.

Technology Technology is used to explore mathematical ideas and as a tool to
solve problems throughout the text.

EXPLORING WITH TECHNOLOGY
Investments that are allowed to grow over time can increase in value surprisingly fast.
Consider the potential growth of $10,000 if earnings are reinvested. More specifically,
suppose A1(t), A2(t), A3(t), A4(t), and A5(t) denote the accumulated values of an investment of $10,000 over a term of t years and earning interest at the rate of 4%, 6%, 8%,
10%, and 12% per year compounded annually.
1. Find expressions for A1(t), A2(t), . . . , A5(t).
2. Use a graphing utility to plot the graphs of A1, A2, . . . , A5 on the same set of
axes, using the viewing window [0, 20] [0, 100,000].

3. Use TRACE to find A1(20), A2(20), . . . , A5(20) and then interpret your results.


xvii

PREFACE

■

Using Technology These are
optional subsections that appear
after the exercises. They can be
used in the classroom if desired
or as material for self-study by
the student. Here the graphing
calculator and Excel spreadsheets are used as a tool to
solve problems. The subsections
are written in the traditional
example-exercise format with
answers given at the back of
the book. Illustrations showing
graphing calculator screens are
extensively used. In keeping with
the theme of motivation through
real-life examples, many sourced
applications are again included.
Students can construct their own
models using real-life data in
Using Technology Section 11.3.
These include models for the

growth of the Indian gaming
industry, the population growth
in the fastest growing metropolitan area in the U.S., and the
growth in online spending,
among others. In Using Technology Section 13.3, students
are asked to predict when the
assets of the Social Security
“trust fund” (unless changes are
made) will be exhausted.

APPLIED EXAMPLE 3 Indian Gaming Industry The following data
gives the estimated gross revenues (in billions of dollars) from the Indian
gaming industries from 1990 (t ϭ 0) to 1997 (t ϭ 7).
Year
Revenue

0

1

2

3

4

5

6

7

0.5

0.7

1.6

2.6

3.4

4.8

5.6

6.8

a. Use a graphing utility to find a polynomial function f of degree 4 that models the
data.
b. Plot the graph of the function f, using the viewing window [0, 8] ϫ [0, 10].
c. Use the function evaluation capability of the graphing utility to compute f(0),
f(1), . . . , f(7) and compare these values with the original data.
Source: Christiansen/Cummings Associates

Solution

a. Choosing P4REG (fourth-order polynomial regression) from the
tistical calculations) menu of a graphing utility, we find

STAT CALC

(sta-

f(t) ϭ 0.00379t 4 Ϫ 0.06616t 3 ϩ 0.41667t 2 Ϫ 0.07291t ϩ 0.48333
FIGURE T3
The graph of f in the viewing window
[0, 8] ϫ [0, 10]

b. The graph of f is shown in Figure T3.
c. The required values, which compare favorably with the given data, follow:
t
f(t)

0

1

2

3

4

5

6

7

0.5

0.8

1.5

2.5

3.6

4.6

5.7

6.8

APPLIED EXAMPLE 3 Solvency of Social Security Fund Unless
payroll taxes are increased significantly and/or benefits are scaled back drastically, it is a matter of time before the current Social Security system goes broke.
Data show that the assets of the system—the Social Security “trust fund”—may be
approximated by
f(t) ϭ Ϫ0.0129t 4 ϩ 0.3087t 3 ϩ 2.1760t 2 ϩ 62.8466t ϩ 506.2955
FIGURE T5
The graph of f ( t )

(0 Յ t Յ 35)

where f(t) is measured in millions of dollars and t is measured in years, with t ϭ 0
corresponding to 1995.
a. Use a graphing calculator to sketch the graph of f.
b. Based on this model, when can the Social Security system be expected to go

broke?
Source: Social Security Administration

Solution

a. The graph of f in the window [0, 35] ϫ [Ϫ1000, 3500] is shown in Figure T5.
b. Using the function for finding the roots on a graphing utility, we find that y ϭ 0
when t Ϸ 34.1, and this tells us that the system is expected to go broke around
2029.


xviii

PREFACE

Exercise Sets The exercise sets are designed to help students understand and apply
the concepts developed in each section. Three types of exercises are included in
these sets.

■

New Concept Questions are
designed to test students’ understanding of the basic concepts
discussed in the section and at
the same time encourage students
to explain these concepts in their
own words.

Exercises provide an ample set
of problems of a routine computational nature followed by an

extensive set of applicationoriented problems.

11.6

Self-Check Exercises

1. Let f(x) ϭ Ϫx 2 Ϫ 2x ϩ 3.
a. Find the derivative f Ј of f, using the definition of the derivative.
b. Find the slope of the tangent line to the graph of f at the
point (0, 3).
c. Find the rate of change of f when x ϭ 0.
d. Find an equation of the tangent line to the graph of f at the
point (0, 3).
e. Sketch the graph of f and the tangent line to the curve at the
point (0, 3).

11.6

2. The losses (in millions of dollars) due to bad loans extended
chiefly in agriculture, real estate, shipping, and energy by the
Franklin Bank are estimated to be
A ϭ f(t) ϭ Ϫt 2 ϩ 10t ϩ 30

(0 Յ t Յ 10)

where t is the time in years (t ϭ 0 corresponds to the beginning of 1994). How fast were the losses mounting at the
beginning of 1997? At the beginning of 1999? At the beginning of 2001?
Solutions to Self-Check Exercises 11.6 can be found on page 676.

Concept Questions

1. Let P(2, f(2)) and Q(2 ϩ h, f(2 ϩ h)) be points on the graph
of a function f.
a. Find an expression for the slope of the secant line passing
through P and Q.
b. Find an expression for the slope of the tangent line passing
through P.
2. Refer to Question 1.
a. Find an expression for the average rate of change of f over
the interval [2, 2 ϩ h].
b. Find an expression for the instantaneous rate of change of
f at 2.

11.6

c. Compare your answers for part (a) and (b) with those of
Exercise 1.
3. a. Give a geometric and a physical interpretation of the
expression
f(x ϩ h) Ϫ f(x)
ᎏᎏ
h
b. Give a geometric and a physical interpretation of the
expression
f(x ϩ h) Ϫ f(x)
lim ᎏᎏ
hǞ0
h
4. Under what conditions does a function fail to have a derivative
at a number? Illustrate your answer with sketches.

Exercises

1. AVERAGE WEIGHT OF AN INFANT The following graph shows the
weight measurements of the average infant from the time of
birth (t ϭ 0) through age 2 (t ϭ 24). By computing the slopes
of the respective tangent lines, estimate the rate of change of
the average infant’s weight when t ϭ 3 and when t ϭ 18. What
is the average rate of change in the average infant’s weight
over the first year of life?
y

2. FORESTRY The following graph shows the volume of wood
produced in a single-species forest. Here f(t) is measured in
cubic meters/hectare and t is measured in years. By computing the slopes of the respective tangent lines, estimate the
rate at which the wood grown is changing at the beginning of
year 10 and at the beginning of year 30.
Source: The Random House Encyclopedia

T2

30
3.5
T1

y
Vo lume of wood produced
(cubic meters/hectare)

■

Self-Check Exercises offer students immediate feedback on
key concepts with worked-out
solutions following the section
exercises.

Average weight of infants (in pounds)

■

6

22.5
20
7.5
5
10
7.5

T2
30
25

10

20
15
10
5

4

t

T1
t

10 12 20
2 4 6 8 10 12 14 16 18 20 22 24
Months
3

y = f(t )

8

30
Years

40

50