College algebra and calculus : an applied approach

1200 Pages·2010·22.54 MB·English

by  Ron Larson

Applications
Biology and Life Sciences Hardy-Weinberg Law,976,985 Plant biology lab,1169
Health Plant growth,1060
Agriculture,495,767,777,995,1020
AIDS cases,1194 Population
Air sacs in the lungs,28
blood oxygen level,108,113 of bees,901
Alligator length,360
blood pressure,1050 of bears,402
Animal shelter,986
body temperature,137,595 of deer,191,332,390,887
Antler spread of an elk,399
epidemic,854,889 of elk,332
Aquaculture,742
exposure to a carcinogen and of fish,339,390,801
Average recycling cost,333,339
mortality,1021 of ring-necked pheasants,926
Bacteria count,233,236,237,254
exposure to sun,742 of sparrows,263
Bacteria growth,351,372,390,392,400,
infant mortality,995 of trout,832
401,402
U.S. HIV/AIDS epidemic,640 Population growth,596,606,752,789,
Bacterial culture,616,759,832,889,986
and wellness,481 794,890,900
Biorhythms,1047,1050
velocity of air flow into and out of Predator-prey cycle,1046,1050,1051
Blue oak,height of,103
the lungs,1050,1070 Psychology
Body mass index (BMI),414
Heart rate,450 Ebbinghaus Model,767
Botany,525,1231
Human height,78,137,188 human memory model,332,333,339,
Calories burned by exercise,495
Hydroflourocarbon emissions,103
360,362,381,399,400,402,880
Carbon dioxide,99,426
Kidney donation,1164
intelligence quotient (IQ),1233
Cardiovascular device sales,1107
Lab practical,1169
IQ scores,136,403
Carnivorous plants,531
Litter of kittens,1230
learning curve,392,401,718,795
Cat cadavers,200 Liver transplants,268
learning theory,759,767,777,781,
Cell division,759 Lung volume,217
786,1195,1205
Clinical trial,19 Medical science
memory experiment,898,900,927
Comparing calories,88 drug concentration,803
Cricket chirps,1224 length of pregnancy,1206 migraine prevalence,580
Crop spraying mixture,437 surface area of a human body,1019 skill retention model,363
Diet supplement,450 velocity of air during coughing,668 sleep patterns,868
Dissections,1168 volume of air in the lungs,867 Stanford-Binet Test,(IQ test),967
E. coli bacterium,length,65 Medicine Ratio of reptiles,1089
Ecology,fencing a study plot,743 amount of drug in bloodstream,594,622 Research study,19
Endangered species population,393,800, bone graft procedures,379 Respiratory diseases,1174
889 days until recovery after a medical Stocking a lake with fish,392,976
Environment procedure,1206,1231 Suburban wildlife,381
contour map of the ozone hole,950 drug absorption,910 Systolic blood pressure,604
oxygen level in a pond,606,686 drug concentration in bloodstream, Tree growth,816
pollutant level,616 300,333,583,686,736,910,1150 Water pollution,332
pollutant removal,546,718,890 duration of an infection,976 Weight of a puppy,182,189
recycling,621,1179 effectiveness of a pain-killing drug,594 Weights of adult male rhesus monkeys,
size of an oil slick,648 healing rate of a wound,353 1203
smokestack emissions,328,339,715 heart transplants,1232
Wheelchair ramp,181
Environmental cost,pollutant removal,557 multiple births,twins,685
Wildlife management,401,718,736
Erosion,38 Poiseuille’s Law,686
Zebrafish embryos,1229
Farming,697 spread of a virus,388,678,801
Fertility rates,668 temperature of a patient,1041
Business and Economics
Fishing quotas,845 treatment of a bacterial infection,1019
Advertising,192
Forest yield,381 Metabolic rate,113
expenses,278,297,301,303,648,
Forestry,624,795,1150 Nutrition,447,986
986,1150
Fruit tree maximum yield,696,740 Optimal area of an archaeological dig
Galloping speeds of animals,370 site,336 Annual
Gardening,825 Orthopedic implant sales,1107 operating cost,136
Genders of children,1181,1194,1229 Oxygen level,61 payroll of new car dealerships,1089
Genetically modified soybeans,438 Peregrine falcons,450 sales,78,251,338,352,414,450,
Genetics,1229 Pest management in a forest,191 1107
Gestation period of rabbits,557 Physiology Average cost,205,206,332,339,677,
Growth of a red oak tree,686 blood flow,845 705,714,716,718,840,1150
Gypsy moths,525 body surface area,736 Average cost and profit,742
Average monthly retail sales,155 Earnings per share,sales,and shareholder Market stabilization,1114
Average production,1012 equity,PepsiCo,996 Marketing,889
Average profit,718,1010 Economics,595 Maximum production level,980,981,
Average revenue,1012 equation of exchange,1018 1019,1021
Average weekly demand,1197 gross domestic product,736 Maximum profit,218,666,701,705,
Average weekly profit,1012 investment,1195 706,719,972,982
Book value per share,205,217 marginal benefits and costs,816 Maximum revenue,698,700,705,706,764
Break-even analysis,136,152,410,411, present value,926 Mean and median useful lifetimes of a
414,440,462 revenue,740 product,1200
Budget analysis,1116 Elasticity of demand,706,719,741 Media selection for advertising,459
Budget deficit,853 Elasticity and revenue,703 Minimum average cost,699,705,719,
Budget variance,7,9 Equimarginal Rule,985 785,786
Cable television companies,496 Expected sales,1185 Minimum cost,695,696,697,706,740,
Capital accumulation,845 Factory production,494,530 977,1019
Capital campaign,880 Federal Mobile homes manufactured,205
Capitalized cost,921,928 cost of food stamps,207 Monthly cost,103,114
Cash flow,825 debt,438 Monthly profit,87
Cash flow per share,Harley-Davidson,791 financial aid awarded,254 Monthly sales,92
Charter bus fares,206 government expenses,19 Monthly flight cost,124
Cobb-Douglas production function,640, Pell Grants,47,414 National defense budget,205
952,955,966,980,1012 Perkins Loans,414 National defense outlays,332
Compact disc shipments,685 student aid,47 National deficit,675
Company profits,146,153 Finance,cyclical stocks,1051 Negotiating a price,606
Comparing profits,235 Flour production,125 Number of Kohl’s stores,901
Comparing sales,236,254 Fuel cost,851 Office space,986
Optimal
Competing restaurants,1169 Furniture production,449
cost,267,336,456,459
Complementary and substitute products, Gold prices,169,217,267
profit,267,336,455,458,459,460,
966 Hotel pricing,494
465,466
Construction,986 Increasing production,646
revenue,266,336,459,465
Consumer and producer surplus,446,449, Increasing profit,143
Owning a franchise,557
464,850,853,854,868,869,900 Insurance,1194
Patents issued,200
Contract bonuses,495 Inventory
Payroll mix-up,1181
Cost,188,235,247,552,580,607,658, cost,677,741
Point of diminishing returns,675,677
668,707,718,728,813,815,816, of digital cameras,1230 Point of equilibrium,422,425,440,462,466
825,845,865,866,976,985,1070, of kayaks,449 Price-earning (P/E) ratio,237
1150,1206 levels,494,530,533 Price of a product,153
Cost-benefit model,328 of liquefied petroleum gases,1069 Production,264,640,865,952,955,985
Cost equation,111 management,557,596 cost,102
Cost,revenue,and profit,204,236,624, of movie players,464 limit,91
647,649,854 replenishment,607 Productivity,677
Daily morning newspapers,number of,993 Job applicants,1168,1170,1229 of a new employee,363
Defective units,1178,1181,1196 Labor/wage requirements,495,507,530 Profit,154,155,170,227,247,268,
Demand,589,590,595,596,606,607, Least-Cost Rule,985 288,297,303,321,337,403,506,
638,640,707,736,742,758,776, Lifetime of a product,1191 595,596,624,625,645,648,658,
785,800,815,832,879,995,1195, Making a sale,1179,1181,1182 668,697,707,728,735,740,741,
1205,1206 Managing a store,607 795,803,816,839,867,900,955,
Manufacturing,1206 975,1019,1107,1156
Demand function,302,351,372,381,
Marginal analysis,731,732,736,742, Profit analysis,656,658
400,825,961
845,909 Projected expenses,90
Depreciation,37,616,750,767,803,
Marginal cost,594,595,596,624,705, Projected profit,151
845,1155
716,833,966,1019 Projected revenue,90,151
Diminishing returns,675,677
Marginal productivity,966 Property tax,190,251
Dividends for Coca-Cola,206
Marginal profit,588,592,594,595,596, Purchasing power of the dollar,193,900
Dollar value,251
624,705 Quality control,9,606,921,1230
Dow Jones Industrial Average,596,678 Marginal revenue,591,594,595,624, Raw materials,505,531
Earnings-dividend ratio,Wal-Mart 705,966,1019 Real estate,1020
Stores,247 Market analysis,1195 Reimbursed expenses,191
Earnings per share,170,929,956 Market research,122,125,152 Returning phone calls,1225
Revenue,181,189,192,218,253,321, Trade deficit,593 Chemistry and Physical Science
338,401,463,566,577,580,595, Transportation cost,300 Acceleration,629,649
707,735,740,795,800,801,804, U.S. currency,381 Acceleration due to gravity,630
832,853,865,868,880,890,900, Useful life,1195,1205,1206,1231 Accuracy of a measurement,133,137,152
975,996,1019,1098,1194,1230 Wages,191,1206,1232 Acid mixture,462
Revenue per share,153,192,300,438, Weekly demand,1190 Acid solution,87
577,613,685,795 Worker’s productivity,395 Acidity of rainwater,1018
Salary contract,557,621 Years of service for employees,1176 Airplane speed,421,424
Sales,136,174,181,251,382,425, Automobile aerodynamics,227
648,678,684,792,795,832,926, Interest Rates Automobile crumple zones,382
1041,1050,1051,1052,1116, Annuity,842,845,867 Average velocity,584
1155,1157,1230 Balance in an account,25,28,39,65, Biomechanics,Froude number,1018
Avon Products,759,868 67,252,372,378,390,402,754, Boiling temperature of water,785
Bausch & Lomb,625 756,1159 Bouncing ball,1116
of concert tickets,449,464 Becoming a millionaire,28 Capacitance in series circuits,92
of e-commerce companies,786 Bond investment,505 Carbon dating,386,392,777,794
of exercise equipment,795 Borrowing money,124,436,481,529 Catenary,763
of gasoline,596 Cash advance,124,152 Charge of an electron,28
Home Depot,622,623 Cash settlement,351 Chemical reaction,395
of insect control products,1089 Certificate of deposit,759 Chemistry experiment,1229
of movie tickets,425 Charitable foundation,921 Circuit analysis,505
of petroleum and coal products,217 College tuition fund,880 Comet orbit,A25,A28
PetSmart,869 Comparing investment returns,90 Dating organic material,746
of prescription drugs by mail order,153 Compound interest,26,47,91,121, Diesel mechanics,247
Procter & Gamble,707 124,146,153,347,348,349,351, Earth and its shape,947,977
Safeway,1077 381,398,546,554,557,616,758, Earthquake magnitude,Richter scale,
Scotts Miracle-Gro,567,580 767,768,775,776,790,794,801, 389,395,401,786
of shoes,425 845,867,1089,1104,1106,1155, Electricity,684
sporting goods,88 1157,1159 Electron microscopes,28
Starbucks,750 Credit card rate,616 Escape velocity,35,38
Sales analysis,607 Doubling time,774,776,804 Estimating speed,38
Sales commission,351 Doubling and tripling an investment,378 Estimating the time of death,395
Sales,equity,and earnings per share, Effective rate of interest,755,758,801 Falling object,97,101,112,114,1098
Johnson & Johnson,1018 Effective yield,794 Eiffel tower,111
Sales growth,677 Endowment,921 Grand Canyon,151
Sales per share,113,206,302,340,392, Finance,777 instantaneous rate of change,585
439,581,613,707 present value,926 on the moon,151
Sales price and list price,191 Future value,758,880 the owl and the mouse,101
Seasonal sales,1057,1069,1070,1076, Inflation rate,26,750,768,803 Royal Gorge Bridge,101
1077,1078 Investment,382,449,463,466,956,967 Fluid flow,A28
Shareholder’s equity,Wal-Mart,956,967 mix,90,414 Geology
Social Security Trust Fund,854 plan,398 contour map of seismic amplitudes,956
State income tax,183 portfolio,424,425,433,437,460,463 crystals,938
State sales tax,183,190 Rule of 70,794 Hot air balloon,112
Straight-line depreciation,186,190,191, strategy,986 Hydrogen orbitals,1232
Ideal Gas Law,91
251,255 time,362,399
Kinetic energy,91
Sugar production,125 Monthly payments,61,953,956
Lensmaker’s equation,92
Supply and demand,425,462 Present value,352,756,758,801,876,
Measurement errors,734,736
Supply function,825 877,880,901,909,921,926,928
Metallurgy,1205
Surplus,446,449,464,850,853,854, of a perpetual annuity,919
Meteorology
868,869,900 Savings plan,44,47
amount of rainfall,1195
Tax liability,285 Scholarship fund,921
annual snowfall in Reno,Nevada,193
Testing for defective units,1226 Simple interest,84,89,91,135,150,181,
atmospheric pressure,956
Total cost,87 190,407,466 average monthly precipitation
Total profit,1098 Stock mix,90 for Bismarck,North Dakota,1070
Total revenue,87,102,113,114,151,154 Tripling time,776 for Sacramento,California,1069
Total sales,112,147,205,1095,1098 Trust fund,758 for San Francisco,California,1077
(continued on back endsheets)
College Algebra and
Calculus
An Applied Approach
R O N L A R S O N
The Pennsylvania State University
The Behrend College
A N N E V. H O D G K I N S
Phoenix College
with the assistance of
DAVID C. FALVO
The Pennsylvania State University
The Behrend College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
College Algebra and Calculus: An Applied Approach © 2010, Brooks/Cole, Cengage Learning
Ron Larson and Anne V. Hodgkins
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1 2 3 4 5 6 7 12 11 10 09 08
Contents iii
Contents
A Word from the Authors (Preface) viii
Textbook Features x
0
Fundamental Concepts of Algebra 1
0.1 Real Numbers: Order and Absolute Value 2
0.2 The Basic Rules of Algebra 10
0.3 Integer Exponents 20
0.4 Radicals and Rational Exponents 29
Mid-Chapter Quiz 39
0.5 Polynomials and Special Products 40
0.6 Factoring 48
0.7 Fractional Expressions 55
Chapter Summary and Study Strategies 62
Review Exercises 64
Chapter Test 67
1
Equations and Inequalities 68
1.1 Linear Equations 69
1.2 Mathematical Modeling 79
1.3 Quadratic Equations 93
1.4 The Quadratic Formula 104
Mid-Chapter Quiz 114
1.5 Other Types of Equations 115
1.6 Linear Inequalities 126
1.7 Other Types of Inequalities 138
Chapter Summary and Study Strategies 148
Review Exercises 150
Chapter Test 154
Cumulative Test: Chapters 0–1 155
2
Functions and Graphs 156
2.1 Graphs of Equations 157
2.2 Lines in the Plane 171
2.3 Linear Modeling and Direct Variation 182
2.4 Functions 194
Mid-Chapter Quiz 207
2.5 Graphs of Functions 208
2.6 Transformations of Functions 219
2.7 The Algebra of Functions 228
2.8 Inverse Functions 238
Chapter Summary and Study Strategies 248
Review Exercises 250
Chapter Test 255
iv Contents
3
Polynomial and Rational Functions 256
3.1 Quadratic Functions and Models 257
3.2 Polynomial Functions of Higher Degree 269
3.3 Polynomial Division 279
3.4 Real Zeros of Polynomial Functions 289
Mid-Chapter Quiz 303
3.5 Complex Numbers 304
3.6 The Fundamental Theorem of Algebra 314
3.7 Rational Functions 322
Chapter Summary and Study Strategies 334
Review Exercises 336
Chapter Test 340
4
Exponential and Logarithmic Functions 341
4.1 Exponential Functions 342
4.2 Logarithmic Functions 354
4.3 Properties of Logarithms 364
Mid-Chapter Quiz 372
4.4 Solving Exponential and Logarithmic Equations 373
4.5 Exponential and Logarithmic Models 383
Chapter Summary and Study Strategies 396
Review Exercises 398
Chapter Test 402
Cumulative Test: Chapters 2–4 403
5
Systems of Equations and Inequalities 404
5.1 Solving Systems Using Substitution 405
5.2 Solving Systems Using Elimination 415
5.3 Linear Systems in Three or More Variables 427
Mid-Chapter Quiz 440
5.4 Systems of Inequalities 441
5.5 Linear Programming 451
Chapter Summary and Study Strategies 461
Review Exercises 462
Chapter Test 466
6
Matrices and Determinants 467
6.1 Matrices and Linear Systems 468
6.2 Operations with Matrices 482
6.3 The Inverse of a Square Matrix 497
Mid-Chapter Quiz 507
6.4 The Determinant of a Square Matrix 508
6.5 Applications of Matrices and Determinants 518
Chapter Summary and Study Strategies 527
Review Exercises 529
Chapter Test 533
Contents v
7
Limits and Derivatives 534
7.1 Limits 535
7.2 Continuity 547
7.3 The Derivative and the Slope of a Graph 558
7.4 Some Rules for Differentiation 569
Mid-Chapter Quiz 581
7.5 Rates of Change: Velocity and Marginals 582
7.6 The Product and Quotient Rules 597
7.7 The Chain Rule 608
Chapter Summary and Study Strategies 619
Review Exercises 621
Chapter Test 625
8
Applications of the Derivative 626
8.1 Higher-Order Derivatives 627
8.2 Implicit Differentiation 634
8.3 Related Rates 641
Mid-Chapter Quiz 649
8.4 Increasing and Decreasing Functions 650
8.5 Extrema and the First-Derivative Test 659
8.6 Concavity and the Second-Derivative Test 669
Chapter Summary and Study Strategies 681
Review Exercises 683
Chapter Test 687
9
Further Applications of the Derivative 688
9.1 Optimization Problems 689
9.2 Business and Economics Applications 698
9.3 Asymptotes 708
Mid-Chapter Quiz 719
9.4 Curve Sketching: A Summary 720
9.5 Differentials and Marginal Analysis 729
Chapter Summary and Study Strategies 739
Review Exercises 740
Chapter Test 743
10
Exponential and Logarithmic Functions 744
10.1 Exponential Functions 745
10.2 Natural Exponential Functions 751
10.3 Derivatives of Exponential Functions 760
Mid-Chapter Quiz 768
10.4 Logarithmic Functions 769
10.5 Derivatives of Logarithmic Functions 778
10.6 Exponential Growth and Decay 787
Chapter Summary and Study Strategies 798
Review Exercises 800
Chapter Test 804
vi Contents
11
Integration and Its Applications 805
11.1 Antiderivatives and Indefinite Integrals 806
11.2 Integration by Substitution and
The General Power Rule 817
11.3 Exponential and Logarithmic Integrals 826
Mid-Chapter Quiz 833
11.4 Area and the Fundamental Theorem of Calculus 834
11.5 The Area of a Region Bounded by Two Graphs 846
11.6 The Definite Integral as the Limit of a Sum 855
Chapter Summary and Study Strategies 863
Review Exercises 865
Chapter Test 869
12
Techniques of Integration 870
12.1 Integration by Parts and Present Value 871
12.2 Partial Fractions and Logistic Growth 881
12.3 Integration Tables 891
Mid-Chapter Quiz 901
12.4 Numerical Integration 902
12.5 Improper Integrals 911
Chapter Summary and Study Strategies 924
Review Exercises 926
Chapter Test 929
13
Functions of Several Variables 930
13.1 The Three-Dimensional Coordinate System 931
13.2 Surfaces in Space 939
13.3 Functions of Several Variables 948
13.4 Partial Derivatives 957
13.5 Extrema of Functions of Two Variables 968
Mid-Chapter Quiz 977
13.6 Lagrange Multipliers 978
13.7 Least Squares Regression Analysis 987
13.8 Double Integrals and Area in the Plane 997
13.9 Applications of Double Integrals 1005
Chapter Summary and Study Strategies 1015
Review Exercises 1017
Chapter Test 1021
14
Trigonometric Functions (online)*
14.1 Radian Measure of Angles
14.2 The Trigonometric Functions
14.3 Graphs of Trigonometric Functions
Mid-Chapter Quiz
14.4 Derivatives of Trigonometric Functions
14.5 Integrals of Trigonometric Functions
Chapter Summary and Study Strategies
Review Exercises
Chapter Test