College Mathematics for Business, Economics, Life Sciences, and Social Sciences For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students with the best possible learning tools This Global Edition preserves the cutting-edge approach and pedagogy of the original, but also features alterations, customization, and adaptation from the North American version Global edition Global edition Global edition THIRTEENTH edition Barnett • Ziegler • Byleen This is a special edition of an established title widely used by colleges and universities throughout the world Pearson published this exclusive edition for the benefit of students outside the United States and Canada If you purchased this book within the United States or Canada, you should be aware that it has been imported without the approval of the Publisher or Author College Mathematics f or Business, Economics, Life Sciences, a nd Social Sciences THIRTEENTH edition R aymond A Barnett • Michael R Ziegler • Karl E Byleen Pearson Global Edition BARNETT_1292057661_mech.indd 16/07/14 11:29 am College Mathematics For Business, Economics, Life Sciences, and Social sciences Thirteenth Edition Global Edition Raymond A Barnett Michael R Ziegler Karl E Byleen Merritt College Marquette University Marquette Universit y Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Editor in Chief: Deirdre Lynch Executive Editor: Jennifer Crum Project Manager: Kerri Consalvo Editorial Assistant: Joanne Wendelken Senior Managing Editor: Karen Wernholm Senior Production Supervisor: Ron Hampton Head of Learning Asset Acquisition, Global Edition: Laura Dent Acquisitions Editor, Global Edition: Subhasree Patra 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page 594, Vario Images/Alamy; page 651, P Amedzro/ Alamy; page 733, Anonymous Donor/Alamy; page 795, Shime/Fotolia; page 838, Aurora Photos/Alamy Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited 2015 The rights of Raymond A Barnett, Michael R Ziegler, and Karl E Byleen to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States edition, entitled College Mathematics for Business, Economics, Life Sciences and Social Sciences, 13th edition, ISBN 978-0-321-94551-8, by Raymond A Barnett, Michael R Ziegler, and Karl E Byleen, published by Pearson Education © 2015 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners ISBN 10: 1-292-05766-1 ISBN 13: 978-1-292-05766-8 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 9 8 7 6 5 4 3 2 1 Typeset in 11 TimesTen-Roman by Integra Publishing Services Printed and bound by Courier Kendallville in The United States of America A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Contents Preface Diagnostic Prerequisite Test 19 Part Chapter A Library of Elementary Functions Linear Equations and Graphs 22 1.1 Linear Equations and Inequalities 23 1.2 Graphs and Lines 32 1.3 Linear Regression 46 Chapter Summary and Review 58 Review Exercises 59 Chapter 2 Functions and Graphs 62 Functions 63 Elementary Functions: Graphs and Transformations 77 Quadratic Functions 89 Polynomial and Rational Functions 104 Exponential Functions 115 Logarithmic Functions 126 Chapter Summary and Review 137 Review Exercises 140 2.1 2.2 2.3 2.4 2.5 2.6 Part Finite Mathematics Chapter 3 Mathematics of Finance 146 Simple Interest 147 Compound and Continuous Compound Interest 154 Future Value of an Annuity; Sinking Funds 167 Present Value of an Annuity; Amortization 175 Chapter Summary and Review 187 Review Exercises 189 3.1 3.2 3.3 3.4 Chapter 4 Systems of Linear Equations; Matrices 193 Review: Systems of Linear Equations in Two Variables 194 Systems of Linear Equations and Augmented Matrices 207 Gauss–Jordan Elimination 216 Matrices: Basic Operations 230 Inverse of a Square Matrix 242 Matrix Equations and Systems of Linear Equations 254 Leontief Input–Output Analysis 262 Chapter Summary and Review 270 Review Exercises 271 4.1 4.2 4.3 4.4 4.5 4.6 4.7 A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Contents Chapter Linear Inequalities and Linear Programming 275 5.1 Linear Inequalities in Two Variables 276 5.2 Systems of Linear Inequalities in Two Variables 283 5.3 Linear Programming in Two Dimensions: A Geometric Approach 290 Chapter Summary and Review 302 Review Exercises 303 Chapter Linear Programming: The Simplex Method 305 6.1 The Table Method: An Introduction to the Simplex Method 306 6.2 The Simplex Method: Maximization with Problem Constraints of the Form … 317 6.3 The Dual Problem: Minimization with Problem Constraints of the Form Ú 333 6.4 Maximization and Minimization with Mixed Problem Constraints 346 Chapter Summary and Review 361 Review Exercises 362 Chapter Logic, Sets, and Counting 365 Logic 366 Sets 374 Basic Counting Principles 381 Permutations and Combinations 389 Chapter Summary and Review 400 Review Exercises 402 7.1 7.2 7.3 7.4 Chapter Probability 405 Sample Spaces, Events, and Probability 406 Union, Intersection, and Complement of Events; Odds 419 Conditional Probability, Intersection, and Independence 431 Bayes’ Formula 445 Random Variable, Probability Distribution, and Expected Value 452 Chapter Summary and Review 461 Review Exercises 463 8.1 8.2 8.3 8.4 8.5 Chapter 9 Markov Chains 467 9.1 Properties of Markov Chains 468 9.2 Regular Markov Chains 479 9.3 Absorbing Markov Chains 489 Chapter Summary and Review 503 Review Exercises 504 A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Contents Part Chapter 10 Calculus Limits and the Derivative 508 Introduction to Limits 509 Infinite Limits and Limits at Infinity 523 Continuity 535 The Derivative 546 Basic Differentiation Properties 561 Differentials 570 Marginal Analysis in Business and Economics 577 Chapter 10 Summary and Review 588 Review Exercises 589 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Chapter 11 Additional Derivative Topics 594 The Constant e and Continuous Compound Interest 595 Derivatives of Exponential and Logarithmic Functions 601 Derivatives of Products and Quotients 610 The Chain Rule 618 Implicit Differentiation 628 Related Rates 634 Elasticity of Demand 640 Chapter 11 Summary and Review 647 Review Exercises 649 11.1 11.2 11.3 11.4 11.5 11.6 11.7 Chapter 12 Graphing and Optimization 651 First Derivative and Graphs 652 Second Derivative and Graphs 668 L’Hôpital’s Rule 685 Curve-Sketching Techniques 694 Absolute Maxima and Minima 707 Optimization 715 Chapter 12 Summary and Review 728 Review Exercises 729 12.1 12.2 12.3 12.4 12.5 12.6 Chapter 13 Integration 733 Antiderivatives and Indefinite Integrals 734 Integration by Substitution 745 Differential Equations; Growth and Decay 756 The Definite Integral 767 The Fundamental Theorem of Calculus 777 Chapter 13 Summary and Review 789 Review Exercises 791 13.1 13.2 13.3 13.4 13.5 A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Contents Chapter 14 Additional Integration Topics 795 Area Between Curves 796 Applications in Business and Economics 805 Integration by Parts 817 Other Integration Methods 823 Chapter 14 Summary and Review 834 Review Exercises 835 14.1 14.2 14.3 14.4 Chapter 15 Multivariable Calculus 838 Functions of Several Variables 839 Partial Derivatives 848 Maxima and Minima 857 Maxima and Minima Using Lagrange Multipliers 865 Method of Least Squares 874 Double Integrals over Rectangular Regions 884 Double Integrals over More General Regions 894 Chapter 15 Summary and Review 902 Review Exercises 905 15.1 15.2 15.3 15.4 15.5 15.6 15.7 Appendix A Basic Algebra Review 908 A.1 A.2 A.3 A.4 A.5 A.6 A.7 Real Numbers 908 Operations on Polynomials 914 Factoring Polynomials 920 Operations on Rational Expressions 926 Integer Exponents and Scientific Notation 932 Rational Exponents and Radicals 936 Quadratic Equations 942 Appendix B Special Topics 951 B.1 Sequences, Series, and Summation Notation 951 B.2 Arithmetic and Geometric Sequences 957 B.3 Binomial Theorem 963 Appendix C Tables 967 Answers 971 Index 1027 Index of Applications 1038 Available separately: Calculus Topics to Accompany Calculus, 13e, and College Mathematics, 13e Chapter A01_BARN7668_13_GE_FM.indd Differential Equations 1.1 Basic Concepts 1.2 Separation of Variables 1.3 First-Order Linear Differential Equations Chapter Review Review Exercises 7/18/14 7:09 PM Contents Chapter Taylor Polynomials and Infinite Series Chapter Probability and Calculus 2.1 Taylor Polynomials 2.2 Taylor Series 2.3 Operations on Taylor Series 2.4 Approximations Using Taylor Series Chapter Review Review Exercises 3.1 Improper Integrals 3.2 Continuous Random Variables 3.3 Expected Value, Standard Deviation, and Median 3.4 Special Probability Distributions Chapter Review Review Exercises Appendixes A and B (Refer to back of College Mathematics for Business, Economics, Life Sciences, and Social Sciences, 13e) Appendix C Tables Appendix D Special Calculus Topic Table III Area Under the Standard Normal Curve D.1 Interpolating Polynomials and Divided Differences Answers Solutions to Odd-Numbered Exercises Index Applications Index A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Preface The thirteenth edition of College Mathematics for Business, Economics, Life Sciences, and Social Sciences is designed for a two-term (or condensed one-term) course in finite mathematics and calculus for students who have had one to two years of high school algebra or the equivalent The book’s overall approach, refined by the authors’ experience with large sections of college freshmen, addresses the challenges of teaching and learning when prerequisite knowledge varies greatly from student to student The authors had three main goals when writing this text: ▶ To write a text that students can easily comprehend ▶ To make connections between what students are learning and how they may apply that knowledge ▶ To give flexibility to instructors to tailor a course to the needs of their students Many elements play a role in determining a book’s effectiveness for students Not only is it critical that the text be accurate and readable, but also, in order for a book to be e ffective, aspects such as the page design, the interactive nature of the presentation, and the ability to support and challenge all students have an incredible impact on how easily students comprehend the material Here are some of the ways this text addresses the needs of students at all levels: ▶ Page layout is clean and free of potentially distracting elements ▶ Matched Problems that accompany each of the completely worked examples help students gain solid knowledge of the basic topics and assess their own level of understanding before moving on ▶ Review material (Appendix A and Chapters and 2) can be used judiciously to help remedy gaps in prerequisite knowledge ▶ A Diagnostic Prerequisite Test prior to Chapter helps students assess their skills, while the Basic Algebra Review in Appendix A provides students with the content they need to remediate those skills ▶ Explore and Discuss problems lead the discussion into new concepts or build upon a current topic They help students of all levels gain better insight into the mathematical concepts through thought-provoking questions that are effective in both small and large classroom settings ▶ Instructors are able to easily craft homework assignments that best meet the needs of their students by taking advantage of the variety of types and difficulty levels of the exercises Exercise sets at the end of each section consist of a Skills Warm-up (four to eight problems that review prerequisite knowledge specific to that section) followed by problems of varying levels of difficulty ▶ The MyMathLab course for this text is designed to help students help themselves and provide instructors with actionable information about their progress The immediate feedback students receive when doing homework and practice in MyMathLab is invaluable, and the easily accessible e-book enhances student learning in a way that the printed page sometimes cannot Most important, all students get substantial experience in modeling and solving real-world problems through application examples and exercises chosen from business and economics, life sciences, and social sciences Great care has been taken to write a book that is mathematically correct, with its emphasis on computational skills, ideas, and problem solving rather than mathematical theory A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM Preface Finally, the choice and independence of topics make the text readily adaptable to a ariety of courses (see the chapter dependencies chart on page 13) This text is one of v three books in the authors’ college mathematics series The others are Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, and Calculus for Business, Economics, Life Sciences, and Social Sciences Additional Calculus Topics, a supplement written to accompany the Barnett/Ziegler/Byleen series, can be used in conjunction with any of these books New to This Edition Fundamental to a book’s effectiveness is classroom use and feedback Now in its thirteenth edition, College Mathematics for Business, Economics, Life Sciences, and Social Sciences has had the benefit of a substantial amount of both Improvements in this edition evolved out of the generous response from a large number of users of the last and previous editions as well as survey results from instructors, mathematics departments, course outlines, and college catalogs In this edition, ▶ The Diagnostic Prerequisite Test has been revised to identify the specific deficiencies in prerequisite knowledge that cause students the most difficulty with finite mathematics and calculus ▶ Most exercise sets now begin with a Skills Warm-up—four to eight problems that review prerequisite knowledge specific to that section in a just-in-time approach References to review material are given for the benefit of students who struggle with the warm-up problems and need a refresher ▶ Section 6.1 has been rewritten to better motivate and introduce the simplex method and associated terminology ▶ Section 14.4 has been rewritten to cover the trapezoidal rule and Simpson’s rule ▶ Examples and exercises have been given up-to-date contexts and data ▶ Exposition has been simplified and clarified throughout the book ▶ MyMathLab for this text has been enhanced greatly in this revision Most notably, a “Getting Ready for Chapter X” has been added to each chapter as an optional resource for instructors and students as a way to address the prerequisite skills that students need, and are often missing, for each chapter Many more improvements have been made See the detailed description on pages 17 and 18 for more information Trusted Features Emphasis and Style As was stated earlier, this text is written for student comprehension To that end, the focus has been on making the book both mathematically correct and accessible to students Most derivations and proofs are omitted, except where their inclusion adds significant insight into a particular concept as the emphasis is on computational skills, ideas, and problem solving rather than mathematical theory General concepts and results are typically presented only after particular cases have been discussed Design One of the hallmark features of this text is the clean, straightforward design of its pages Navigation is made simple with an obvious hierarchy of key topics and a judicious use of call-outs and pedagogical features We made the decision to maintain a two-color d esign to A01_BARN7668_13_GE_FM.indd 7/18/14 7:09 PM ... of Demand 640 Chapter 11 Summary and Review 647 Review Exercises 649 11 .1 11. 2 11 .3 11 .4 11 .5 11 .6 11 .7 Chapter 12 Graphing and. .. 11 x 1 + = 13 y -5 M 01_ BARN7668 _13 _GE_C 01. indd 30 m 12 . - = 3 x 14 . -4 15 2u + = 5u + - 7u 16 . - 3y + + y = 13 - 8y 17 10 x + 251x - 32 = 275 18 . - 314 - x2 = - 1x + 12 19 - y … 41y - 32... Act 19 88 Authorized adaptation from the United States edition, entitled College Mathematics for Business, Economics, Life Sciences and Social Sciences, 13 th edition, ISBN 978-0-3 21- 945 51- 8, by