Business Precalculus - OpenTextBookStore

1 Business Precalculus Edition David Lippman ii Copyright 2016 David Lippman This text is licensed under a Creative Commons Attribution-Share Alike United States License. To view a copy of this license, visit or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. You are free: to Share to copy, distribute, display, and perform the work to Remix to make derivative works Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).

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3 The best way to do this is with a link to this web page: Chapters 1 3 are remixed from Precalculus : an investigation of functions , 2015 David Lippman and Melonie Rasmussen, under the Creative Commons Attribution Share-Alike license. Chapter 4 is remixed from College Algebra, 2015 Rice University, produced by OpenStax College, under a Creative Commons Attribution license. Download the original for free at Chapter 5 contains portions remixed from My the Numbers, Milos Podmanik, under the Creative Commons Attribution Non-Commercial Share-Alike license, and from Applied Finite Math Rupinder Sekhon, under the Creative Commons Attribution license.

4 Chapter 6 8 are remixed from Math in Society, 2015 David Lippman, under the Creative Commons Attribution Share-Alike license. iii About the Author David Lippman received his master s degree in mathematics from Western Washington University and has been teaching at Pierce College since Fall 2000. David has been long time advocate of open learning, open materials, and basically any idea that will reduce the cost of education for students. It started by supporting the college s calculator rental program, and running a book loan scholarship program. Eventually the frustration with the escalating costs of commercial text books and the online homework systems that charged for access led him and his colleagues to take action.

5 First, David developed IMathAS, open source online math homework software that runs and Through this platform, he became an integral part of a vibrant sharing and learning community of teachers from around Washington State that support and contribute to WAMAP. Those pioneering efforts, supported by dozens of other dedicated faculty and financial support from the Transition Math Project, led to a system used by thousands of students every quarter, saving hundreds of thousands of dollars over comparable commercial offerings. David continued further and wrote his first open textbook, Math in Society, a math for liberal arts majors book, after being frustrated by students having to pay $100+ for a textbook for a terminal course.

6 Frustrated by both cost and the style of commercial texts, David and colleague Melonie Rasmussen began writing Precalculus : an investigation of functions in 2010. This text pulls in portions from Precalculus , Math in Society, and other open textbooks, and adapts them to have the Business focus desired for a Business Precalculus or finite math course. This text serves as preparation for Applied Calculus, a Business -focused brief calculus text coauthored by Shana Calaway, Dale Hoffman, and David. Supplements Online homework and video lesson sets to accompany this text are available on iv Table of Contents Chapter 1: functions and Lines .. 1 Section functions and Function Notation.

7 1 Section Domain and Range .. 10 Section Rates of Change and Behavior of Graphs .. 19 Section Linear functions .. 27 Section Graphs of Linear functions .. 34 Section Modeling with Linear functions .. 45 Section Fitting Linear Models to Data .. 53 Chapter 2: Systems of Equations and Matrices .. 59 Section Systems of Equations .. 59 Section Solving Systems using Matrices .. 76 Section Matrix Operations .. 90 Section Solving Systems with Inverses .. 101 Chapter 3: Linear Programming .. 115 Section Inequalities in One Variable .. 115 Section Linear Inequalities .. 125 Section Graphical Solutions .. 131 Section Simplex Method.

8 140 Section Applications of Linear Programming .. 146 Chapter 4: Polynomial and Rational functions .. 153 Section Quadratic functions .. 153 Section Polynomial functions .. 164 Section Rational functions .. 175 Chapter 5: Exponential and Logarithmic functions .. 185 Section Exponential functions .. 185 Section Logarithmic functions .. 199 Section Exponential and Logarithmic Models .. 211 Chapter 6: Finance .. 221 Section Simple and Compound Interest .. 221 Section Annuities .. 230 Section Payout Annuities .. 235 Section Loans .. 239 Section Multistage Finance Problems .. 246 Chapter 7: Sets .. 253 Section Sets .. 253 Section Venn Diagrams and Cardinality.

9 258 Chapter 8: Probability .. 265 Section Concepts of Probability .. 265 Section Conditional Probability and Bayes Theorem .. 275 Section Counting .. 283 Section Expected Value .. 296 1 This chapter is part of Business Precalculus David Lippman 2016. This content is remixed from Precalculus : an investigation of functions Lippman & Rasmussen 2011. This material is licensed under a Creative Commons CC-BY-SA license. Chapter 1: functions and Lines Section functions and Function Notation .. 1 Section Domain and Range .. 10 Section Rates of Change and Behavior of Graphs .. 19 Section Linear functions .. 27 Section Graphs of Linear functions .

10 34 Section Modeling with Linear functions .. 45 Section Fitting Linear Models to Data .. 53 Section functions and Function Notation What is a Function? The natural world is full of relationships between quantities that change. When we see these relationships, it is natural for us to ask If I know one quantity, can I then determine the other? This establishes the idea of an input quantity, or independent variable, and a corresponding output quantity, or dependent variable. From this we get the notion of a functional relationship in which the output can be determined from the input. For some quantities, like height and age, there are certainly relationships between these quantities.