INSTRUCTOR S RESOURCE GUIDE AND SOLUTIONS …

1 INSTRUCTOR S RESOURCE GUIDE AND SOLUTIONS MANUAL ELKA M. BLOCK FRANK PURCELL FINITE MATHEMATICS AND CALCULUS WITH APPLICATIONS NINTH EDITION Margaret L. Lial American River College Raymond N. Greenwell Hofstra University Nathan P. Ritchey Youngstown State University Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness.

2 The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Reproduced by Pearson from electronic files supplied by the author. Copyright 2012, 2009, 2005 Pearson Education, Inc. Publishing as Pearson, 75 Arlington Street, Boston, MA 02116. 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 the prior written permission of the publisher.

3 Printed in the United States of America. ISBN-13: 978-0-321-74626-9 ISBN-10: 0-321-74626-0 CONTENTS iii CONTENTS PREFACE .. xi HINTS FOR TEACHING FINITE MATHEMATICS AND CALCULUS WITH APPLICATIONS .. xiii PRETESTS .. xxix ANSWERS TO PRETESTS .. xxxvi FINAL EXAMINATIONS .. xxxvii ANSWERS TO FINAL EXAMINATIONS .. lxiii SOLUTIONS TO ALL EXERCISES CHAPTER R ALGEBRA REFERENCE Polynomials .. 1 Factoring .. 3 Rational Expressions.

4 4 Equations .. 7 Inequalities .. 13 Exponents .. 23 Radicals .. 27 CHAPTER 1 LINEAR FUNCTIONS Slopes and Equations of Lines .. 31 Linear Functions and Applications .. 43 The Least Squares Line .. 50 Chapter Review Exercises .. 62 Extended Application: Using Extrapolation to Predict Life Expectancy .. 69 iv CONTENTS CHAPTER 2 SYSTEMS OF LINEAR EQUATIONS AND MATRICES Solution of Linear Systems by the Echelon Method.

5 71 Solution of Linear Systems by the Gauss-Jordan Method .. 82 Addition and Subtraction of Matrices .. 108 Multiplication of Matrices .. 113 Matrix Inverses .. 122 Input-Output Models .. 141 Chapter Review Exercises .. 149 Extended Application: Contagion .. 165 CHAPTER 3 LINEAR PROGRAMMING: THE GRAPHICAL METHOD Graphing Linear Inequalities .. 167 Solving Linear Programming Problems Graphically .. 176 Applications of Linear Programming .. 183 Chapter Review Exercises .. 192 Extended Application: Sensitivity Analysis .. 200 CHAPTER 4 LINEAR PROGRAMMING: THE SIMPLEX METHOD Slack Variables and the Pivot.

6 203 Maximization Problems .. 209 Minimization Problems; 233 Nonstandard Problems .. 249 Chapter Review Exercises .. 268 Extended Application: Using Integer Programming in the Stock-Cutting Problem .. 283 CONTENTS v CHAPTER 5 MATHEMATICS OF FINANCE Simple and Compound 285 Future Value of an Annuity .. 296 Present Value of an Annuity; Amortization .. 306 Chapter Review Exercises .. 321 Extended Application: Time, Money, and Polynomials.

7 331 CHAPTER 6 LOGIC Statements .. 333 Truth Tables and Equivalent Statements .. 338 The Conditional and Circuits .. 344 More on the Conditional .. 354 Analyzing Arguments and Proofs .. 358 Analyzing Arguments with Quantifiers .. 363 Chapter Review Exercises .. 373 Extended Application: Logic Puzzles .. 379 CHAPTER 7 SETS AND PROBABILITY Sets .. 385 Applications of Venn Diagrams .. 390 Introduction to Probability .. 405 Basic Concepts of 411 Conditional Probability; Independent Events .. 422 Bayes Theorem .. 434 Chapter Review Exercises .. 448 Extended Application: Medical Diagnosis .. 462 vi CONTENTS CHAPTER 8 COUNTING PRINCIPLES The Multiplication Principle; Permutations.

8 463 Combinations .. 468 Probability Applications of Counting Principles .. 477 Binomial Probability .. 486 Probability Distributions; Expected Value .. 495 Chapter Review Exercises .. 505 Extended Application: Optimal Inventory for a Service Truck .. 518 CHAPTER 9 STATISTICS Frequency Distributions; Measures of Central Tendency .. 519 Measures of Variation .. 525 The Normal Distribution .. 531 Normal Approximation to the Binomial Distribution .. 541 Chapter Review Exercises .. 550 Extended Application: Statistics in the Law The Castaneda Decision .. 558 CHAPTER 10 NONLINEAR FUNCTIONS Properties of Functions .. 559 Quadratic Functions; Translation and Reflection.

9 569 Polynomial and Rational Functions .. 585 Exponential Functions .. 597 Logarithmic Functions .. 607 Applications: Growth and Decay; Mathematics of Finance .. 618 Chapter 10 Review Exercises .. 627 Extended Application: Power Functions .. 643 CONTENTS vii CHAPTER 11 THE DERIVATIVE Limits .. 645 Continuity .. 658 Rates of Change .. 664 Definition of the Derivative .. 677 Graphical Differentiation.

10 696 Chapter 11 Review Exercises .. 700 Extended Application: A Model for Drugs Administered Intravenously .. 713 CHAPTER 12 CALCULATING THE DERIVATIVE Techniques for Finding Derivatives .. 715 Derivatives of Products and Quotients .. 725 The Chain Rule .. 735 Derivatives of Exponential Functions .. 745 Derivatives of Logarithmic Functions .. 758 Chapter 12 Review Exercises .. 770 Extended Application: Electric Potential and Electric 782 CHAPTER 13 GRAPHS AND THE DERIVATIVE Increasing and Decreasing Functions .. 785 Relative Extrema .. 798 Higher Derivatives, Concavity, and the Second Derivative Test.