College Algebra and Calculus: An Applied Approach

1600 Pages·2013·79.34 MB·English

by  Ron Larson

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Applications
BIOLOGY AND LIFE SCIENCES Population growth,600,609,788,792,801,884
Psychology
Agriculture,971
learning curve,396,407,718,793
Antler spread of an elk,405
learning theory,758,766,775,780,785,800
Bacteria count,235,238,247,368,408
migraine prevalence,585
Bacteria growth,356,396,407,408
sleep patterns,857
Bacterial culture,619,741,751,758,829,964
Stanford-Binet Test (IQ test),946
Blood oxygen level,108,112
Recycling,325,333,625
Blue oak height,103
Research study,19
Body length of a baby girl,113
Body mass index (BMI),419 Rocky Mountain spotted fever,388
Botany,528 Shannon diversity index,955
Calories burned by exercise,500 Skill retention model,366
Carbon dioxide in the atmosphere,431 Stocking a lake with fish,955
Clinical trial,19 Suburban wildlife,385
Crop spraying mixture,441 Systolic blood pressure,607
Diet supplement,452,453 Tree growth,687,813
Dissections,582 Venus flytrap growth,536
Environment Weight of a puppy,183,190
contour map of the ozone hole,935 Wildlife management,735
oxygen level in a pond,61,609,687 Wind chill,38
pollutant removal,333,552,561,715,718,740
BUSINESS
size of an oil slick,650
Fertility rates,669 Advertising awareness,610
Fish diet,741 Advertising expenses,271,281,290,294,650,964
Flea,consumption of a,39 Average cost,678,705,714,718,740,837
Forensics,79 Average production,987
Forest yield,385 Average profit,718,985,987,995
Forestry,Doyle Log Rule,627 Average revenue,987,995
Fruit production,499 Average salary,of public school nurses,749
Galloping speeds of animals,376 Bolts produced by a foundry,830
Gardening,442,822 Break-even analysis,137,154,415,418,419,467
Gestation period of rabbits,562 Budget deficit,851
Gypsy moths,527 Budget variance,7,9
Hair growth rate,192 Capital accumulation,842
Hardy-Weinberg Law,955 Capital campaign,876
Health,486 Capitalized cost,903
body temperature,137,599 Certificate of deposit,758
epidemic,850 Charitable foundation,903
nutrition,450,964 Cobb-Douglas production function,643,931,934,945,959,987
U.S. HIV/AIDS epidemic,643 Complementary and substitute products,945
Heart rate,453 Construction,964
Hospital patients,271 Consumer and producer surplus,449,452,470,847,850,851,
Human height,137 865,866,884
Human memory model,325,333,364,366,385,405,406,408,876 Contract bonuses for football players,500
Intelligence,207 Cost,207,213,219,237,547,558,562,585,610,619,660,669,
Kidney transplants,261 718,810,812,813,822,842,863,864,955,963,994
Lead concentration in human bones,345 Cost,revenue,and profit,206,649,651,851,865
Lung volume,218 Cost-benefit model,320
Maximum yield of trees,697,739,766 Demand,594,609,641,643,707,735,741,757,776,784,799,
Medical science,velocity of air during coughing,669 800,822,829,876,885,940,970,994
Medicine Demand function,294,295,355,356,368,385,406
amount of drug in bloodstream,598 Depreciation,37,619,749,766,793,842
drug absorption,894 Diminishing returns,676
drug concentration in bloodstream,588,687,735,749,801 Dividends for Coca-Cola,207
duration of an infection,955 Dow Jones Industrial Average,600,679
Poiseuille’s Law,687 Earnings per share
spread of a virus,392,799 Apple,935
Metabolic rate of a beetle,113 Hewlett-Packard,993
Morris water maze,171 Earnings-dividend ratio of Wal-Mart Stores,345
Native prairie grasses,385 Economics,599,813
Nesting falcons,453 Elasticity,703,706,718,739,742
Optimal area of an archaeological dig site,330 Equimarginal Rule,963
Pest management in a forest,192 Finance,776
Physiology,body surface area,741 Fuel cost,600,848,850
Population,324,333,394,397,407,408,799,829 Furniture production,452
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Hotel pricing,499 of skiing facilities,802
Hourly wages,192 Symantec Corporation,219
Increasing production,648 Texas Roadhouse,864
Increasing profit,143 Under Armour,572,584,829
Inventory,452,470,500,535,538,562,610,678 Revenue per share
Investment income of Aflac,155 Amazon.com,294,443
Labor wage requirements,500,512,535 California Pizza Kitchen,193
Least-Cost Rule,963 Google,443
Marginal analysis,731,734,735,741,841,892 U.S. Cellular,616
Marginal cost,598,599,627,830,945,993 Revenues per share,revenues,and shareholder’s equity,
Marginal productivity,945 McDonald’s,971
Marginal profit,593,596,599,600,610,627 Salary contract,562,624
Marginal revenue,595,598,599,627,945,994 Sales,650,679,790,793,884
Market research,125,154 Advance Auto Parts,830
Maximum production level,959,960 Aéropostale,190
Maximum profit,667,687,701,705,706,718,739,951,961 Apple,175
Maximum revenue,698,700,705,706,739,763 Bed Bath & Beyond,332
Media selection for advertising,462 Best Buy,970
Minimum average cost,699,705,719,739,784,801 The Clorox Company,707
Minimum cost,696,697,706,956 of concert tickets,452,470
Monthly cost,103,124 CVS Caremark Corporation,628
Monthly sales,92 of doughnuts,137
Office space,964 of DVDs,295
Operating cost for a fleet of vans,135 of e-readers,501
Optimal fourth quarter,182
cost,260,330,459,462 of gasoline,600
profit,260,330,458,461,462,463,471,472 Green Mountain Coffee Roasters,112
revenue,259,330,462,471 Intuit Corp.,245
Owning a franchise,562 Lockheed Martin Corporation,707
Point of diminishing returns,676,678,687 Men’s Wearhouse,865
Point of equilibrium,427,430,444,468,472 Oracle Corp.,79
Price,of a product,155 Perrigo Company,407
Price-earnings (P/E) ratio PetSmart,866
DISH Network,239 quarterly,245
Walt Disney,239 Scotts Miracle-Gro Company,572,585
Production,643,862,931,934,963,994,996 of shoes,430
cost,102 Tractor Supply Company,626
daily,499,535 of two restaurants,238
limit,91,114 Walgreen Company,147,749
Productivity,399,678 Wal-Mart,660
Profit,146,155,156,229,237,238,260,261,281,296,331, WebMD Health Corp.,453
345,599,627,628,647,650,660,669,685,687,696,728, Sales per share
735,741,812,836,864,934,954,994 Columbia Sportswear,586
Johnson & Johnson,206 Dollar Tree,616
maximum,218,219 Hershey’s,442
Medco Health Solutions,799 Hormel Foods,334
Profit analysis,658,660 Microsoft Corporation,582
Purchasing power,193 Ross Stores,419
Quality control,9,609,903 Tiffany & Co.,686
Raw materials,510,536 TJX Companies,419
Real estate,995 Shareholder’s equity
Revenue,102,113,114,153,156,313,707,735,793,813,822, Sketchers,935,946
829,850,862,865,876,884,885,894,954,994 Wal-Mart,993
Buffalo Wild Wings,113 Stores
Cablevision Systems Corporation,829 AutoZone,182
California Pizza Kitchen,193 BJ’s Wholesale Club,431
Chipotle Mexican Grill,686 CVS,416
Cintas,686 Family Dollar,171
Costco Wholesale,332 PetSmart,536
and demand,812 Safeway,152
DIRECTV,511 Walgreen Company,416
eBay,636 Wal-Mart,398
of Harry Potter movies,89 Straight-line depreciation,191,245,248
of James Cameron movies,153 Supply,430,650,822
McDonald’s,582 Tax liability,278
Panera Bread Company,798 Trademarks issued,442
P.F. Chang’s China Bistro,910 Transportation costs,293
Research in Motion,357 Value of a product,191,245
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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COLLEGE ALGEBRA
and CALCULUS
An Applied Approach
Second Edition
Ron Larson
The Pennsylvania State University
The Behrend College
Anne V. Hodgkins
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
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College Algebra and Calculus: An Applied Approach © 2013, 2010, Brooks/Cole, Cengage Learning
Second Edition
ALL RIGHTS RESERVED. No part of this work covered by the copyright
Ron Larson herein may be reproduced, transmitted, stored, or used in any form or by
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Cover Designer: Larson Texts, Inc. ISBN-13: 978-1-133-10506-0
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Contents
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
Quiz Yourself 39
0.5 Polynomials and Special Products 40
Project: Population 47
0.6 Factoring 48
0.7 Fractional Expressions 55
Algebra Tutor 62
Summary and Study Strategies 64
Review Exercises 66
Test Yourself 68
1
Equations and Inequalities 69
1.1 Linear Equations 70
1.2 Mathematical Modeling 80
1.3 Quadratic Equations 93
1.4 The Quadratic Formula 104
Project: Revenue 113
Quiz Yourself 114
1.5 Other Types of Equations 115
1.6 Linear Inequalities 126
1.7 Other Types of Inequalities 138
Algebra Tutor 148
Summary and Study Strategies 150
Review Exercises 152
Test Yourself 156
2
Functions and Graphs 157
2.1 Graphs of Equations 158
2.2 Lines in the Plane 172
2.3 Linear Modeling and Direct Variation 183
2.4 Functions 195
Project: Expenditures 207
Quiz Yourself 208
2.5 Graphs of Functions 209
2.6 Transformations of Functions 220
2.7 The Algebra of Functions 230
Algebra Tutor 240
Summary and Study Strategies 242
Review Exercises 244
Test Yourself 248
iii
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iv Contents
3
Polynomial and Rational Functions 249
3.1 Quadratic Functions and Models 250
3.2 Polynomial Functions of Higher Degree 262
3.3 Polynomial Division 272
3.4 Real Zeros of Polynomial Functions 282
Project: Sales 295
Quiz Yourself 296
3.5 Complex Numbers 297
3.6 The Fundamental Theorem of Algebra 306
3.7 Rational Functions 314
Algebra Tutor 326
Summary and Study Strategies 328
Review Exercises 330
Test Yourself 334
4
Exponential and Logarithmic Functions 335
4.1 Inverse Functions 336
4.2 Exponential Functions 346
Project: Drug Concentration 357
4.3 Logarithmic Functions 358
Quiz Yourself 368
4.4 Properties of Logarithms 369
4.5 Solving Exponential and Logarithmic Equations 377
4.6 Exponential and Logarithmic Models 387
Algebra Tutor 400
Summary and Study Strategies 402
Review Exercises 404
Test Yourself 408
5
Systems of Equations and Inequalities 409
5.1 Solving Systems Using Substitution 410
5.2 Solving Systems Using Elimination 420
5.3 Linear Systems in Three or More Variables 432
Project: Revenues Per Share 443
Quiz Yourself 444
5.4 Systems of Inequalities 445
5.5 Linear Programming 454
Algebra Tutor 464
Summary and Study Strategies 466
Review Exercises 467
Test Yourself 472
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Contents v
6
Matrices and Determinants 473
6.1 Matrices and Linear Systems 474
6.2 Operations with Matrices 487
Project: Sales of e-Readers 501
6.3 The Inverse of a Square Matrix 502
Quiz Yourself 512
6.4 The Determinant of a Square Matrix 513
6.5 Applications of Matrices and Determinants 521
Algebra Tutor 530
Summary and Study Strategies 532
Review Exercises 534
Test Yourself 538
7
Limits and Derivatives 539
7.1 Limits 540
7.2 Continuity 553
7.3 The Derivative and the Slope of a Graph 563
7.4 Some Rules for Differentiation 574
Quiz Yourself 586
7.5 Rates of Change: Velocity and Marginals 587
7.6 The Product and Quotient Rules 601
7.7 The Chain Rule 611
Algebra Tutor 620
Summary and Study Strategies 622
Review Exercises 624
Test Yourself 628
8
Applications of the Derivative 629
8.1 Higher-Order Derivatives 630
Project: Median Prices of U.S. Homes 636
8.2 Implicit Differentiation 637
8.3 Related Rates 644
Quiz Yourself 651
8.4 Increasing and Decreasing Functions 652
8.5 Extrema and the First-Derivative Test 661
8.6 Concavity and the Second-Derivative Test 670
Algebra Tutor 680
Summary and Study Strategies 682
Review Exercises 684
Test Yourself 688
9
Further Applications of the Derivative 689
9.1 Optimization Problems 690
9.2 Business and Economic Applications 698
9.3 Asymptotes 708
Project: Alternative-Fueled Vehicles 718
Quiz Yourself 719
9.4 Curve-Sketching: A Summary 720
9.5 Differentials and Marginal Analysis 729
Algebra Tutor 736
Summary and Study Strategies 738
Review Exercises 739
Test Yourself 742
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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vi Contents
10
Derivatives of Exponential and Logarithmic Functions 743
10.1 Exponential Functions 744
10.2 Natural Exponential Functions 750
10.3 Derivatives of Exponential Functions 759
Quiz Yourself 767
10.4 Logarithmic Functions 768
10.5 Derivatives of Logarithmic Functions 777
10.6 Exponential Growth and Decay 786
Project: Cell Phone Subscribers 793
Algebra Tutor 794
Summary and Study Strategies 796
Review Exercises 798
Test Yourself 802
11
Integration and Its Applications 803
11.1 Antiderivatives and Indefinite Integrals 804
11.2 Integration by Substitution and The General Power Rule 814
11.3 Exponential and Logarithmic Integrals 823
Quiz Yourself 830
11.4 Area and the Fundamental Theorem of Calculus 831
11.5 The Area of a Region Bounded by Two Graphs 843
Project: Social Security 851
11.6 The Definite Integral as the Limit of a Sum 852
Algebra Tutor 858
Summary and Study Strategies 860
Review Exercises 862
Test Yourself 866
12
Techniques of Integration 867
12.1 Integration by Parts and Present Value 868
12.2 Integration Tables 878
Project: Purchasing Power of the Dollar 884
Quiz Yourself 885
12.3 Numerical Integration 886
12.4 Improper Integrals 895
Algebra Tutor 904
Summary and Study Strategies 906
Review Exercises 908
Test Yourself 910
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.