INSTRUCTOR’S RESOURCE AND SOLUTIONS MANUAL ELKA BLOCK FRANK PURCELL
FINITE MATHEMATICS AND CALCULUS WITH APPLICATIONS TENTH EDITION
Margaret L. Lial American River College
Raymond N. Greenwell Hofstra University
Nathan P. Ritchey Edinboro University
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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. 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. Copyright © 2016, 2012, 2008 Pearson Education, Inc. Publishing as Pearson, 501 Boylston 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. Printed in the United States of America. ISBN-13: 978-0-13-393401-4 ISBN-10: 0-13-393401-2
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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 R.1 Polynomials .............................................................................................................................................................. 1 R.2 Factoring .................................................................................................................................................................. 3 R.3 Rational Expressions ................................................................................................................................................ 4 R.4 Equations .................................................................................................................................................................. 8 R.5 Inequalities ............................................................................................................................................................. 14 R.6 Exponents ............................................................................................................................................................... 24 R.7 Radicals .................................................................................................................................................................. 28 CHAPTER 1 LINEAR FUNCTIONS 1.1 Slopes and Equations of Lines ................................................................................................................................ 33 1.2 Linear Functions and Applications ......................................................................................................................... 46 1.3 The Least Squares Line........................................................................................................................................... 54 Chapter 1 Review Exercises .......................................................................................................................................... 66 Extended Application: Using Extrapolation to Predict Life Expectancy ...................................................................... 74
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CHAPTER 2 SYSTEMS OF LINEAR EQUATIONS AND MATRICES 2.1 Solution of Linear Systems by the Echelon Method ............................................................................................... 77 2.2 Solution of Linear Systems by the Gauss-Jordan Method ...................................................................................... 89 2.3 Addition and Subtraction of Matrices ................................................................................................................... 117 2.4 Multiplication of Matrices .................................................................................................................................... 122 2.5 Matrix Inverses ..................................................................................................................................................... 132 2.6 Input-Output Models ............................................................................................................................................. 151 Chapter 2 Review Exercises ........................................................................................................................................ 160 Extended Application: Contagion ............................................................................................................................... 176 CHAPTER 3 LINEAR PROGRAMMING: THE GRAPHICAL METHOD 3.1 Graphing Linear Inequalities ................................................................................................................................ 177 3.2 Solving Linear Programming Problems Graphically ............................................................................................ 186 3.3 Applications of Linear Programming.................................................................................................................... 195 Chapter 3 Review Exercises ........................................................................................................................................ 206 Extended Application: Sensitivity Analysis................................................................................................................ 214 CHAPTER 4 LINEAR PROGRAMMING: THE SIMPLEX METHOD 4.1 Slack Variables and the Pivot ............................................................................................................................... 217 4.2 Maximization Problems ........................................................................................................................................ 223 4.3 Minimization Problems; Duality ........................................................................................................................... 247 4.4 Nonstandard Problems .......................................................................................................................................... 264 Chapter 4 Review Exercises ........................................................................................................................................ 283 Extended Application: Using Integer Programming in the Stock-Cutting Problem ................................................... 298
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CHAPTER 5 MATHEMATICS OF FINANCE 5.1 Simple and Compound Interest ............................................................................................................................. 301 5.2 Future Value of an Annuity .................................................................................................................................. 313 5.3 Present Value of an Annuity; Amortization .......................................................................................................... 323 Chapter 5 Review Exercises ........................................................................................................................................ 339 Extended Application: Time, Money, and Polynomials ............................................................................................. 348 CHAPTER 6 LOGIC 6.1 Statements ............................................................................................................................................................. 351 6.2 Truth Tables and Equivalent Statements............................................................................................................... 356 6.3 The Conditional and Circuits ................................................................................................................................ 362 6.4 More on the Conditional ....................................................................................................................................... 372 6.5 Analyzing Arguments and Proofs ......................................................................................................................... 377 6.6 Analyzing Arguments with Quantifiers ................................................................................................................ 382 Chapter 6 Review Exercises ........................................................................................................................................ 392 Extended Application: Logic Puzzles ......................................................................................................................... 398 CHAPTER 7 SETS AND PROBABILITY 7.1 Sets........................................................................................................................................................................ 405 7.2 Applications of Venn Diagrams ............................................................................................................................ 410 7.3 Introduction to Probability .................................................................................................................................... 426 7.4 Basic Concepts of Probability ............................................................................................................................... 431 7.5 Conditional Probability; Independent Events ....................................................................................................... 443 7.6 Bayes’ Theorem .................................................................................................................................................... 456 Chapter 7 Review Exercises ........................................................................................................................................ 471 Extended Application: Medical Diagnosis.................................................................................................................. 485
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CHAPTER 8 COUNTING PRINCIPLES 8.1 The Multiplication Principle; Permutations .......................................................................................................... 487 8.2 Combinations ........................................................................................................................................................ 492 8.3 Probability Applications of Counting Principles................................................................................................... 501 8.4 Binomial Probability ............................................................................................................................................. 511 8.5 Probability Distributions; Expected Value ............................................................................................................ 519 Chapter 8 Review Exercises ........................................................................................................................................ 530 Extended Application: Optimal Inventory for a Service Truck .................................................................................. 542 CHAPTER 9 STATISTICS 9.1 Frequency Distributions; Measures of Central Tendency ..................................................................................... 545 9.2 Measures of Variation ........................................................................................................................................... 552 9.3 The Normal Distribution ....................................................................................................................................... 560 9.4 Normal Approximation to the Binomial Distribution ........................................................................................... 570 Chapter 9 Review Exercises ........................................................................................................................................ 581 Extended Application: Statistics in the Law—The Castaneda Decision .................................................................... 589
CHAPTER 10 NONLINEAR FUNCTIONS 10.1 Properties of Functions .................................................................................................................................. 591 10.2 Quadratic Functions; Translation and Reflection ........................................................................................... 602 10.3 Polynomial and Rational Functions ............................................................................................................... 619 10.4 Exponential Functions.................................................................................................................................... 632 10.5 Logarithmic Functions ................................................................................................................................... 642 10.6 Applications: Growth and Decay; Mathematics of Finance........................................................................... 655 Chapter 10 Review Exercises .................................................................................................................................. 663 Extended Application: Power Functions .................................................................................................................. 679
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