College algebra : with applications for business and the life sciences : Instructor's annotated edition

763 Pages·2009·11.39 MB·English

by  Ron Larson

College Algebra
with Applications for Business
and the Life Sciences
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 HOUGHTON MIFFLIN
COMPANY
Boston New York
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We have included examples and exercises that use real-life data as well as technology
output from a variety of software. This would not have been possible without the help of
many people and organizations. Our wholehearted thanks goes to all for their time and
effort.
Trademark acknowledgments:TI and CBR are registered trademarks of Texas
Instruments,Inc. Excel is a registered trademark of Microsoft Corporation.
Cover image:©Ann Manner/Getty Images
Copyright ©2009 by Houghton Mifflin Company. All rights reserved.
No part of this work may be reproduced or transmitted in any form or by any means,electronic
or mechanical,including photocopying and recording,or by any information storage or retrieval
system,without the prior written permission of Houghton Mifflin Company unless such copy-
ing is expressly permitted by federal copyright law. Address inquiries to College Permissions,
Houghton MifflinCompany,222 Berkeley Street,Boston,MA 02116-3764.
Printed in the U.S.A.
Library of Congress Control Number:2007937005
ISBNs
Instructor’s Annotated Edition:
ISBN-13:978-0-547-06999-9
ISBN-10:0-547-06999-5
For orders,use student text ISBNs:
ISBN-13:978-0-547-05269-4
ISBN-10:0-547-05269-3
1 2 3 4 5 6 7 8 9–DOW–11 10 09 08 07
Contents iii
Contents
A Word from the Authors (Preface) vi
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
Sequences, Series, and Probability 534
7.1 Sequences and Summation Notation 535
7.2 Arithmetic Sequences and Partial Sums 545
7.3 Geometric Sequences and Series 554
7.4 The Binomial Theorem 563
Mid-Chapter Quiz 570
7.5 Counting Principles 571
7.6 Probability 581
7.7 Mathematical Induction 593
Chapter Summary and Study Strategies 604
Review Exercises 606
Chapter Test 610
Cumulative Test: Chapters 5–7 611
Appendices A1
Appendix A: An Introduction to Graphing Utilities A1
Appendix B: Conic Sections A8
B.1 Conic Sections A8
B.2 Conic Sections and Translations A20
Appendix C: Further Concepts in Statistics*
C.1 Data and Linear Modeling
C.2 Measures of Central Tendency and Dispersion
Answers A29
Index I1
*For Appendix C and other resources, please visit
college.hmco.com/info/larsonapplied.
vi A Word from the Authors
From the Desks of Ron Larson and Anne Hodgkins . . .
Do you have students who are taking college algebra as their last college
math course, or students who are majoring in subjects such as biology and
business and plan to go on to applied calculus?
The truth is,many of us are teaching bothtypes of students in one classroom.
We realized that we had to change the way we thought about this course in order
to reach this diverse audience more effectively and ensure their success.
The result:College Algebra with Applications for Business and the Life Sciences.
We’re excited about this new textbook because it acknowledges where students
are when they enter the course . . . and where they should be when they complete
it. We review the basic algebra that students have studied previously (in Chapter 0
and in the exercises,notes,study tips,and study sheets throughout the text),and
we present a solid college algebra course that balances understanding of concepts
with the development of strong problem-solving skills. When students have
finished with this text, they will be fully prepared to study—and succeed in—
applied calculus.
This new textbook program helps students learn the math in the ways we have
found most effective for our students,by practicing their problem-solving skills
and reinforcing their understanding in the context of actual problems they
may encounter in their lives and their careers.
And we’re also excited about this textbook program because it is being published
as part of a whole series of textbooks tailored to the needs of college algebra and
applied calculus students majoring in business,biology,and related courses.
College Algebra with Applications for Business and the Life Sciences
Calculus:An Applied Approach,8e
Brief Calculus:An Applied Approach,8e
Calculus with Applications for the Life Sciences
College Algebra and Calculus:An Applied Approach
We hope you and your students enjoy College Algebra with Applications for
Business and the Life Sciences. Feel free to tell us what you think about it. Over
the years, we have received many useful comments from both instructors and
students,and we value these comments very much.
Ron Larson
Anne V. Hodgkins
Preface vii
Goals for This Text
Establish a Solid Foundation in College Algebra
To help students master algebra concepts, many effective tools are incorporated
throughout the text. These features help students evaluate and reinforce their
understanding of the math.
■ After each worked-out Example, a Checkpoint offers the opportunity for
immediate practice.
■ At the end of each section and before the Section Exercises,a Concept Check
poses noncomputational questions designed to test students’basic understand-
ing of that section’s concepts.
■ Each exercise set begins with a Skills Reviewof cumulative exercises that test
prerequisite skills from earlier sections.
■ The Mid-Chapter Quiz offers frequent opportunities for self-assessment so
students can discover any topics they might need to study further before they
progress too far into the chapter.
■ The Chapter Summarysummarizes skills presented in the chapter and corre-
lates each skill to Review Exercises for extra practice.
■ The Study Strategies provide invaluable tips for overcoming common study
obstacles.
■ The Chapter Testenables students to identify and strengthen any weaknesses
before taking an exam.
Present Real-World Problems to Motivate Interest and
Understanding
Applications have been culled from news sources, current events, industry data,
world events,and government data. Students see algebra as relevant to the world
around them; if they plan to continue their study of math and go on to calculus,
the extensive opportunities to create and interpret models from real data provide
solid preparation.
Enhance Understanding Using Technology
Students can visualize the math by using powerful technology,such as graphing
calculators and spreadsheet software,and so develop a deeper comprehension of
mathematical concepts.
■ Optional Technology boxesfeature exercises that offer students opportunities
to practice using these tools.
■ The iconin the exercises suggestswhen a graphing calculator or other tech-
nology tool can be used.
■ The icon appears when spreadsheet software,such as Excel,especially rel-
evant to business students,can be incorporated.
viii Preface
Prepare for Success in Applied Calculus and Beyond
Several text features pique students’interest by using everyday examples to extend
practice in modeling. Honing these skills will improve students’proficiency and
help ensure success in their future careers.
■ Make a Decision exercises ask students open-ended questions as they apply
concepts to real-world problems.
■ Business Capsules highlight business situations in actual companies and
encourage students to include research as part of their problem solving.
■ Extended Applications are in-depth, applied exercises requiring students to
work with large data sets. They often involve work in creating or analyzing mod-
els. These exercises are offered online at college.hmco.com/info/larsonapplied.
Acknowledgments ix
Acknowledgments
We would like to thank our colleagues who have helped us develop this program.
Their encouragement,criticisms,and suggestions have been invaluable to us.
Reviewers
Michael Brook,University of Delaware
Tim Chappell,Metropolitan Community College–Penn Valley
Warrene Ferry,Jones County Junior College
David Frank,University of Minnesota
Michael Frantz,University of La Verne
Linda Herndon,OSB,Benedictine College
Ruth E. Hoffman,Toccoa Falls College
Eileen Lee,Framingham State College
Shahrokh Parvini,San Diego Mesa College
Jim Rutherfoord,Chattahoochee Technical College
Laurie Varecka,University of Arizona
Portions of College Algebra with Applications for Business and the Life Sciences
have been featured in our previously published College Algebra: Concepts and
Models. We thank the following reviewers, who have given us many useful
insights throughout that book’s five editions:
Rosalie Abraham,Florida Community College at Jacksonville;Judith A.
Ahrens,Pellissippi State Technical Community College;Sandra Beken,
Horry-Georgetown Technical College;Diane Benjamin,University of
Wisconsin–Platteville;Dona Boccio,Queensborough Community College;
Kent Craghead,Colby Community College;Carol Edwards,St. Louis
Community College at Florissant Valley;Thomas L. Fitzkee,Francis Marion
University;Michael Frantz,University of La Verne;Nick Geller,Collin
College;Carolyn H. Goldberg,Niagara County Community College;Carl
Hughes,Fayetteville State University;Buddy A. Johns,Wichita State
University;Annie Jones,Calhoun State Community College;Steven Z. Kahn,
Anne Arundel Community College;Claire Krukenberg,Eastern Illinois
University;John Kubicek,Southwest Missouri State University;Charles G.
Laws,Cleveland State Community College;John A. Lewallen,Southeastern
Louisiana University;Gael Mericle,Minnesota State University Mankato;
Michael Montano,Riverside Community College;Sue Neal,Wichita State
University;Terrie L. Nichols,Cuyamaca College;Mark Omodt,Anoka-Ramsey
Community College;G. Bryan Stewart,Tarrant County College;Jacqueline
Stone,University of Maryland;David Surowski,Kansas State University;
Pamela K. Trim,Southwest Tennessee Community College;Jamie Whitehead,
Texarkana College
In addition, we would like to thank the staff of Larson Texts, Inc., who assisted
in preparing the manuscript,rendering the art package,and typesetting and proof-
reading the pages and supplements.
On a personal level, we would like to thank our families, especially Deanna
Gilbert Larson and Jay N. Torok, for their love, patience, and support. Also,
special thanks goes to R. Scott O’Neil.