Applied Calculus - Applied Calculus 5e.pdf

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L IST OF A PPLICATIONS
BUSINESS AND ECONOMICS
Accumulated value of an income stream,
564
Accumulation years of baby boomers, 219
Advertising, 100, 172, 272, 309, 370, 513,
605, 640
Age distribution of company directors, 754
Ailing financial institutions, 148, 169
Airport traffic, 593
Alternative energy sources, 514
Amusement park attendance, 218, 564
Annuities, 526, 532
Assembly time of workers, 315, 430
Auto interest rates, 496
Auto operating costs, 644
Auto replacement parts market, 101
Average age of cars in U.S., 341
Demand for RNs, 317
Demand for wine, 413
Depletion of Social Security funds, 353, 355
Depreciation, 101, 411, 499
Designing a cruise ship pool, 657
Determining the optimal site, 635
Digital TV services, 52
Digital TV shipments, 107
Disposable annual incomes, 100
Document management, 100
Driving costs, 134
Driving range of an automobile, 13
Housing prices, 401, 497, 647
Housing starts, 89, 222, 254
Illegal ivory trade, 101
Incomes of American families, 405, 414
Income streams, 590
Increase in temporary workers, 195
Indian gaming industry, 105
Inflation, 244
Installment contract sales, 546
Internal rate of return, 843, 847
International email usage, 100
Inventory control and planning, 148, 363,
364, 367
Investment analysis, 399, 402, 524, 525
Investment groups, 847
Investment options, 402
Investment returns, 402, 556
IQs, 610
IRAs, 526, 532
Effect of a tax cut on spending, 803, 805,
851
Effect of advertising on hotel revenue, 317
Effect of advertising on sales, 100, 172, 195,
309, 315, 317, 434, 514
Effect of housing starts on jobs, 222
Effect of inflation on salaries, 402
Effect of inventory and floor space on
profit, 667
Effect of luxury tax on consumption, 221
Effect of mortgage rates on housing starts,
89, 272
Effect of price increase on quantity de-
manded, 271
Effect of TV advertising on car sales, 514
Efficiency studies, 194, 317, 487
Elasticity of demand, 233, 235, 238, 239,
258
Energy conservation, 503, 509
Energy consumption and productivity, 148,
401
Energy efficiency of appliances, 412
Establishing a trust fund, 591, 851
Expected demand, 437
Expressway tollbooths, 738
Banking, 66, 315, 453
Black Monday, 321
Book design, 366
Box office receipts, 133, 207, 338
Business cycles, 878, 882, 894
Keeping with the traffic flow, 80
Keogh accounts, 546
Cable ad revenue, 107
Cable TV subscription, 275, 452, 499
Capacity of a man-made lake, 542
Capital value, 592, 807
CDs, 401
City planning, 137, 207
Coal production, 498, 546
Cobb-Douglas production function, 615,
620, 658, 689
COLAs, 73
Commissions, 149
Commodity prices, 49, 52, 149, 413
Commuter airlines, 554
Compact disc sales, 556
Comparison of bank rates, 402
Complementary commodities, 617, 621, 689
Computer security costs, 91
Construction costs, 108
Construction jobs, 89, 209
Consumer decisions, 35
Consumer demand, 195, 206, 272, 370, 437
Consumer price index, 195, 244, 310, 402
Consumers’ surplus, 521, 531, 546, 563
Consumption function, 73
Consumption of electricity, 483
Consumption of petroleum, 577
Cost of laying cable, 31, 35
Cost of producing calculators, 320
Cost of producing guitars, 452
Cost of producing loudspeakers, 345
Cost of producing solar cell panels, 460
Cost of producing surfboards, 172
Cost of removing toxic waste, 206, 333, 338
Creation of new jobs, 222
Crop yield, 170, 415
Cruise ship bookings, 223
Land prices, 621, 686
Laser disc sales, 201
Launching a fighter aircraft, 453
Life span of light bulbs, 733, 743
Linear depreciation, 73, 101
Loan amortization, 415, 607
Loan consolidation, 402
Locating a power station, 635
Locating a TV relay station, 633
Lorentz curves, 528, 532, 547, 564
Magazine circulation, 449
Mail-order phone sales, 738
Management decisions, 317, 525
Manufacturing capacity, 79, 298, 319
Manufacturing capacity operating rate, 349
Manufacturing costs, 88
Marginal average cost function, 227, 228,
235, 236, 237
Marginal cost function, 224, 226, 235, 236,
237, 487
Marginal productivity of labor and capital,
615, 621
Marginal productivity of money, 659
Marginal profit, 231, 487
Marginal propensity to consume, 237
Marginal propensity to save, 238
Marginal revenue, 230, 236, 487, 545
Market equilibrium, 96, 103, 106, 521, 546
Market share, 171, 450
Markup on a car, 13
Mass transit subsidies, 645
Maximizing crop yield, 366, 708
Maximizing production, 413, 661
Maximizing profit, 345, 351, 352, 631, 634,
635, 655, 660
Maximizing revenue, 352, 353
Maximizing sales, 661
Maximum capacity of an oil well, 413
Median price of homes, 647
Meeting profit goals, 14
Minimizing construction costs, 365, 367, 661
Factory worker wages, 766, 837
Federal budget deficit, 81, 284
Female self-employed workforce, 351
Financing a college education, 402, 532
Financing a home, 270, 272, 607
Forecasting commodity prices, 272
Forecasting profits, 272, 317
Forecasting sales, 100, 461
Franchises, 531, 556, 564
Fuel economy of cars, 192, 278, 578
Fuel tank capacity of a space shuttle, 540
Gasoline prices, 329
Gasoline self-service sales, 69
Gender gap, 72
Gross domestic product, 172, 191, 245, 265,
269, 313, 338, 353
Growth of bank deposits, 66
Growth of HMOs, 193, 556
Growth of service industries, 579, 723, 785
Health-care spending, 196
Health club membership, 181, 215
Home mortgages, 607, 847
Home sales, 193, 299
Home-shopping industry, 68, 153
Hotel occupancy rate, 89, 222, 897
Demand for agricultural commodities, 272
Demand for computer software, 594
Demand for electricity, 646
Demand for perfume, 413, 569
Demand for personal computers, 222, 434
Minimizing container costs, 661
Minimizing heating and cooling costs, 636
Minimizing production costs, 346, 352, 366
Minimizing shipping costs, 35
Morning traffic rush, 299
Mortgage rates, 562
Multimedia sales, 247, 319
Multiplier effect, 803, 805, 851
Sales promotions, 412
Sales tax, 73
Shopping habits, 753
Sinking funds, 527, 714
Size of average farm, 645
Social Security beneficiaries, 156
Social Security contributions, 51
Social Security wage base, 645
Solvency of the Social Security system, 336,
353, 355
Stock prices, 881, 889, 894
Substitute commodities, 617, 621
Supply and demand, 102, 103, 172, 196, 255,
258, 268, 272
Educational level of senior citizens, 48, 643
Effect of budget cuts on crime rate, 316
Effect of immigration on population
growth, 714
Endowments, 591, 595, 804
Energy conservation, 509
Energy needs, 483, 546
Female life expectancy, 220, 464
Net-connected computers in Europe, 648
Net investment flow, 498, 697
Net sales, 644
Newsmagazine shows, 464
Nielsen television polls, 152, 170
Gender gap, 72
Global epidemic, 487
Grade distributions, 767
Growth of HMOs, 319
Oil production, 498, 553
Oil shortage, 329
Oil spills, 222, 464, 574, 595
Online banking, 648
Online shopping, 196
Online spending, 107
Operating costs of a truck, 265
Optimal charter flight fare, 366
Optimal selling price, 413
Optimal speed of a truck, 367
Optimal subway fare, 360
Tax-deferred annuities, 402
Tax planning, 402
Television pilots, 737
Testing new products, 248
Time intervals between phone calls, 738
Time on the market, 319, 355
Training personnel, 714
Tread-lives of tires, 581
Truck leasing, 73
Trust funds, 591
Health-care spending, 87, 196, 648
HMOs, 92
Immigration, 432
Increase in juvenile offenders, 415
Index of environmental quality, 370
Learning curves, 74, 141, 148, 207, 269, 295,
430, 434, 464, 714
Logistic curves, 431
VCR ownership, 564
Male life expectancy, 221
Marijuana arrests, 107, 489
Mass transit, 360
Packaging, 108, 361, 365, 635, 749, 763
Pensions, 401, 402
Perpetual net income stream, 591
Perpetuities, 589, 807
Personal consumption expenditure, 237
Population density, 679, 685
Portable phone services, 196, 648
Present value of an income stream, 531
Price-earnings ratio, 668
Prime interest rate, 148
Producers’ surplus, 521, 531, 546, 564, 579
Product design, 366
Product life, 738, 753
Product reliability, 766, 767, 837
Production costs, 236
Production of steam coal, 555
Productivity fueled by oil, 413
Productivity of a country, 621
Projected Provident funds, 295
Wages, 167
Waiting times, 737, 740, 741, 745, 738
Warranties, 767
Wilson lot size formula, 607
Worker efficiency, 73, 100, 194, 317, 338,
370, 483
World production of coal, 498
Worldwide networked PCs, 275
Worldwide production of vehicles, 219
Narrowing gender gap, 51
Oil spills, 222, 464, 574
Overcrowding of prisons, 88, 300
Percentage of households with VCRs, 435
Percentage of population relocating, 413
Percentage of women in the labor force,
415
Politics, 74
Population growth, 73, 134, 195, 207, 209,
453, 489, 514, 547, 713
Population growth in the 21st century, 435
Prison population, 106
Yield of an apple orchard, 108
SOCIAL SCIENCES
Age of drivers in crash fatalities, 295
Air pollution, 221, 295, 299, 320, 352, 452,
579, 785
Alcohol-related traffic accidents, 556
Arson for profit, 606
Quality of environment, 370
Quality control, 13, 452
Recycling programs, 564
Research funds, 591
Bursts of knowledge, 141
Rate of bank failures, 247, 298, 355
Rate of return on investment, 556
Real estate, 402, 410, 476, 497, 578, 621
Reliability of microprocessors, 738, 795
Reliability of robots, 738
Resale value, 433, 545
Restaurant revenue, 878, 882, 894
Retirement planning, 401, 402
Reverse annuity mortgage, 532
Civil service exams, 767
Closing the gender gap in education, 72
College admissions, 51, 644
Commuter trends, 360, 545
Continuing education enrollment, 221, 463,
785
Cost of removing toxic waste, 202, 333, 338
Crime, 245, 272, 291, 353
Cube rule, 74
Curbing population growth, 195
SAT scores, 644
Scholarship funds, 589
Spread of rumor, 413, 435, 714, 725
Student enrollment, 463
Television viewing, 464
Thurstone learning models, 181, 222
Toxic pollutants, 206
Traffic studies, 194, 196, 222, 299
TV viewing patterns, 170, 221
Sales forecasts, 52, 181, 545, 644
Sales growth and decay, 46, 464
Sales of digital signal processors, 196
Sales of digital TV’s, 101
Sales of handheld computers, 487
Sales of prerecorded music, 72
Sales of video games, 594
Decline of union membership, 80
Diffusion of information, 435
Distribution of families by size, 737
Distribution of incomes, 14, 405, 528, 532
Driving age requirements, 755
U.S. Census, 248, 487
Vacation trends, 785
Voter registration, 564
Waste generation, 647
Welfare costs, 645
World population growth, 415, 433, 713
Harbor cleanup, 74
Celsius and Fahrenheit temperature, 13
Coast guard patrol search mission, 259
Ideal height–weights for women, 51
Importance of time in treating heart at-
tacks, 208
IV systems, 149
Designing a grain silo, 367
Driving costs, 95
LIFE SCIENCES
Absorption of drugs, 416
AIDS in Massachusetts, 501
Air inhaled during respiration, 880, 894
Allometric growth, 698, 705
Amount of glucose in the bloodstream, 698,
704
Anticipated rise in number of Alzheimer’s
patients, 78, 246
Arterial blood flow, 668
Arteriosclerosis, 217, 222
Average weights and heights of infants,
169, 464, 762
Effect of an earthquake on a structure, 885
Effect of stopping on average speed, 194
Endowments, 806
Length of a hospital stay, 770
Lengths of infants, 579
Life span of a plant, 738, 752
Finding the position of a planet, 883
Fisk’s law, 698, 704
Flight of a rocket, 189, 195, 256, 295, 320,
348, 351, 453
Flight path of a plane, 153
Force generated by a centrifuge, 611
Nuclear fallout, 434
Oxygen content of a pond, 131, 202, 338,
352
Ozone pollution, 453
Gridlock, 222
Poiseuille’s law, 73, 606
Predator–prey population, 865, 870, 877,
881, 897
Preservation of species, 189
Pulse rates, 222, 513
Blood alcohol level, 413
Blood pressure, 390, 870
Brentano-Stevens Law, 725
IQs, 610, 767
Keeping with the traffic flow, 80
Carbon-14 dating, 428, 434
Carbon monoxide in the air, 85, 193, 221,
462
Cardiac output, 565, 573, 581
Clark’s rule, 181
Concentration of a drug in an organ, 465
Concentration of a drug in the blood-
stream, 133, 206, 295, 338, 435, 464,
496, 499, 555, 697
Conservation of species, 195, 244
Contraction of the trachea during a cough,
346
Cowling’s rule, 100
Cricket chirping and temperature, 101
Crop yield, 170
Lambert’s law of absorption, 697, 713
Launching a fighter aircraft, 453
Lotteries, 532
Quality of environment, 370
Radioactive decay, 427, 433, 434, 697
Reaction of a frog to a drug, 100
Reaction to a drug, 353
Residual effect of a drug, 804, 807
Magnitude of an earthquake, 390
Mortgage payments, 270
Motion of a maglev, 111, 155, 243, 451
Senior citizen’s health care, 101
Serum cholesterol levels, 765, 835
Speed of a chemical reaction, 134
Spread of HIV, 193
Surface area of a honeycomb, 883
Surface area of a horse, 272
Surface area of a single-celled organism, 73
Surface area of the human body, 453, 606,
624, 668
Newton’s law of cooling, 434, 498, 698, 713,
725
Number of daylight hours in Chicago, 893
Postal regulations, 74, 365, 366
Probability of snowfall, 738, 753
Doomsday situation, 133
Drug dosages, 100, 206
Reaction time of a motorist, 753
Rings of Neptune, 266, 271
Effect of bactericide, 170, 206
Effect of enzymes on chemical reactions,
338
Energy expended by a fish, 149, 353
Epidemic models, 413, 431, 434, 563, 710
Eradication of polio, 412
Exponential decay, 433, 704
Extinction situation, 414
Toxic pollutants, 133
Transmission of disease, 795
Sound intensity, 390
Speedboat racing, 487
Stimulus response, 693
Stopping distance of a racing car, 195
Strength of a beam, 366
Unclogging arteries, 269
Velocity of blood, 194, 353
Televising a rocket launch, 882
Terminal velocity, 332
Tracking a criminal suspect, 882
Travel time, 35
Trial run of an attack submarine, 578
Turbo-charged engine performance, 514
Walking vs. running, 103
Water pollution, 206, 315
Weight of whales, 51
Whale population, 189, 499
Female life expectancy, 220
Flights of birds, 367
Flow of blood in an artery, 453, 499, 886
Forensic science, 390
Forestry, 169, 295
Formaldehyde levels, 207
Friend’s rule, 73
GENERAL INTEREST
Acceleration of a car, 245, 453
Area of a Norman window, 108, 366
Atmospheric pressure, 390
Average highway speed of a vehicle, 196,
295
Used car markup, 13
Velocity of a car, 172, 451, 499
Velocity of a dragster, 555
Volume of a football, 541
VTOL aircraft, 245
Gompertz Growth Curve, 445, 698, 714
Growth of a cancerous tumor, 194, 269
Growth of bacteria, 172, 217, 426, 433, 713
Growth of fruit fly population, 121, 434,
564, 714
Growth rate of a species population, 697
Blowing soap bubbles, 259
Boston Marathon, 293
Boyle’s law, 73
Water level in a harbor, 882
Weber-Fechner law, 711
Applied Calculus
for the Managerial, Life, and Social Sciences
F IFTH E DITION
S. T. Tan
Stonehill College
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Library of Congress Cataloging-in-Publication Data
Canada
Tan, Soo Tang.
Applied calculus for the managerial, life, and social
sciences / S. T. Tan.—5th ed.
p. cm.
Includes index.
Rev. ed. of: College mathematics. 4th ed.
1999.
ISBN 0-534-37843-9
1. Calculus.
I. Tan, Soo Tang. Applied calculus.
II. Title.
QA303.T14
2002
515—dc21
2001025725
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