Student Solutions Manual for College Algebra in Context with Applications for the Managerial, Life, and Social Sciences

Description

Table of Contents

1. Functions, Graphs, and Models; Linear Functions
   • Algebra Toolbox
   • 1-1 Functions and Models
   • 1-2 Graphs of Functions
   • 1-3 Linear Functions
   • 1-4 Equations of Lines
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 1 Skills Check
   • Chapter 1 Review
   • Group Activities/Extended Applications
2. Linear Models, Equations, and Inequalities
   • Algebra Toolbox
   • 2-1 Algebraic and Graphical Solution of Linear Equations
   • 2-2 Fitting Lines to Data Points: Modeling Linear Functions
   • 2-3 Systems of Linear Equations in Two Variables
   • 2-4 Solutions of Linear Inequalities
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 2 Skills Check
   • Chapter 2 Review
   • Group Activities/Extended Applications
3. Quadratic, Piecewise-Defined, and Power Functions
   • Algebra Toolbox
   • 3-1 Quadratic Functions; Parabolas
   • 3-2 Solving Quadratic Equations
   • 3-3 Power and Root Functions
   • 3-4 Piecewise-Defined Functions and Power Functions
   • 3-5 Quadratic and Power Models
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 3 Skills Check
   • Chapter 3 Review
   • Group Activities/Extended Applications
4. Additional Topics with Functions
   • Algebra Toolbox
   • 4-1 Transformations of Graphs and Symmetry
   • 4-2 Combining Functions; Composite Functions
   • 4-3 One-to-One and Inverse Functions
   • 4-4 Additional Equations and Inequalities
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 4 Skills Check
   • Chapter 4 Review
   • Group Activities/Extended Applications
5. Exponential and Logarithmic Functions
   • Algebra Toolbox
   • 5-1 Exponential Functions
   • 5-2 Logarithmic Functions; Properties of Logarithms
   • 5-3 Exponential and Logarithmic Equations
   • 5-4 Exponential and Logarithmic Models
   • 5-5 Exponential Functions and Investing
   • 5-6 Annuities; Loan Repayment
   • 5-7 Logistic and Gompertz Functions
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 5 Skills Check
   • Chapter 5 Review
   • Group Activities/Extended Applications
6. Higher-Degree Polynomial and Rational Functions
   • Algebra Toolbox
   • 6-1 Higher-Degree Polynomial Functions
   • 6-2 Modeling with Cubic and Quartic Functions
   • 6-3 Solution of Polynomial Equations
   • 6-4 Polynomial Equations Continued; Fundamental Theorem of Algebra
   • 6-5 Rational Functions and Rational Equations
   • 6-6 Polynomial and Rational Inequalities
   • Preparing for Calculus
   • Summary
   • Key Concepts and Formulas
   • Chapter 6 Skills Check
   • Chapter 6 Review
   • Group Activities/Extended Applications
7. Systems of Equations and Matrices
   • Algebra Toolbox
   • 7-1 Systems of Linear Equations in Three Variables
   • 7-2 Matrix Solution of Systems of Linear Equations
   • 7-3 Matrix Operations
   • 7-4 Inverse Matrices; Matrix Equations
   • 7-5 Determinants and Cramer’s Rule
   • 7-6 Systems of Nonlinear Equations
   • Summary
   • Key Concepts and Formulas
   • Chapter 7 Skills Check
   • Chapter 7 Review
   • Group Activities/Extended Applications
8. Special Topics in Algebra
   • 8-1 Systems of Inequalities
   • 8-2 Linear Programming: Graphical Methods
   • 8-3 Sequences and Discrete Functions
   • 8-4 Series
   • 8-5 The Binomial Theorem
   • 8-6 Conic Sections: Circles and Parabolas
   • 8-7 Conic Sections: Ellipses and Hyperbolas
   • Summary
   • Key Concepts and Formulas
   • Chapter 8 Skills Check
   • Chapter 8 Review
   • Group Activity/ Extended Applications

Appendices

1. Basic Graphing Calculator Guide
2. Basic Guide to Excel 2010 and Excel 2013

Credits

Answers to Selected Exercises

Index

Hallmark applications

• Real-data applications reflect recent economic and financial changes, and prepare students to solve problems in their future courses and varied careers.
• Each section begins with a motivational problem that presents a real-life scenario. The problem is solved after the necessary skills are presented in that section.
• Special business and finance models are included to demonstrate the applications of functions to the business world.
• Group Activities and Extended Applications encourage communication skills and collaborative learning by asking students to apply their knowledge in creative ways.
• NEW / UPDATED – More than 250 problems have been replaced with new or updated problems, to keep the real data applications current.
• NEW – Additional modeling problems that involve decision making and critical thinking have been added throughout the text.
• Chapter openers begin with a brief application that shows how the upcoming material relates to the real world. To motivate the students to read the text, each chapter opener also includes a list of applications students will see in each section.

Tools for skill-building and review

• NEW – A Corequisite Notebook by Lisa Yocco is now available to complement this text. It includes all Algebra Toolbox topics with unique exercises for practice, followed by small group activities to enhance classroom time. The activities portion of the notebook was created by Trisha Sholar.
• NEW / REVISED – Each Algebra Toolbox at the beginning of every chapter has been expanded and strengthened to reflect corequisite course content, with more than 80 new exercises. 
• The Algebra Toolbox provides a just-in-time review of the algebra needed to learn upcoming material. Each Algebra Toolbox begins with a list of Key Concepts, just like the sections in the book, to make this tool even more useful for students.
• NEW – Additional topics include calculations and properties of real numbers; operations with fractions; evaluating algebraic expressions; solving basic linear equations; evaluating formulas for given values; operations with radicals; rationalizing denominators; operations with complex numbers.
• Specific steps for additional topics have been added to Appendix A.
• NEW – Preparing for Calculus sections have been added before the Chapter Summaries in Chapters 1 through 6. These sections present approximately 100 problems that use skills from each chapter in calculus contexts, to demonstrate the importance of algebra for those who will be taking calculus.
• Key Concepts are outlined at the beginning of every section. These lists are consistent with the order and organization of the material in the chapter reviews, providing a helpful cross-reference for exam preparation.
• Skills Check problems precede the exercise sets, allowing students to quickly check if they have read and understood all the concepts needed to complete their homework.
• Exercise sets are designed to test student comprehension by incorporating the algebraic skills covered in the Skills Check with the application problems they will encounter in the real world.
• Chapter review material includes a wealth of resources to help students study efficiently.
• A chapter summary and grid outline Key Concepts and Formulas, which are organized by section and point back to the Key Concepts list at the beginning of each section.
• Skills Check problems and the exercise sets test students’ comprehension of the material in the chapter.
• The Note-Taking Guide provides a framework for students as they take notes for this course. Students have a guide to help them organize definitions, examples, and processes. The guide is available for download in MyLab Math and also as a print supplement.

Content changes

• REVISED – Section 3.3 from the previous edition is now divided into two new sections:
• The new Section 3.3 expands coverage of power functions and root functions, and new Section 3.4 expands coverage of piecewise-defined functions and absolute-value functions. 
• These sections have many more examples and exercises than in the 5th Edition.
• REVISED – More specific Excel steps have been added within the Spreadsheet Solutions in the text, with references to Appendix B for more details. 
• Specific steps for additional topics have been added to Appendix B.
• NEW – Discussion of loan amortization using graphing calculators has been added to Chapter 5, and the detailed steps for solving loan amortization problems with graphing calculators have been added to Appendix A.
• NEW – Discussion of loan amortization using Excel has been added to Chapter 5, and the detailed steps for solving loan amortization problems with Excel has been added to Appendix B. 

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math 

MyLab Math is the teaching and learning platform that empowers you to reach every student. By combining trusted 

author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

• Exercise sets develop students’ problem-solving skills to prepare them for their future courses and careers. Exercise sets incorporate modeling techniques, application problems, and real data.
• Learning aids in the exercises—Help Me Solve This, View an Example, and wrong-answer feedback—offer extra support for students who need help remembering definitions and explaining processes. These may be turned off at the instructor’s discretion.
• Author-designated sample homework problems are available in MyLab Math to make your start-up time efficient.
• Guided Visualizations bring mathematical concepts to life. These animated figures help students visualize the concepts through directed explorations and purposeful manipulation. Guided Visualizations are assignable in MyLab Math and encourage active learning, critical thinking, and conceptual learning.
• The Note-taking Guide is a workbook that provides a framework for students as they take notes for this course. Students have a guide to help them organize definitions, examples, and processes. The guide is available for download in MyLab Math and also as a print supplement.
• Narrated Example Videos have been updated to reflect new content and current real data.
• Introductory Videos contain a brief overview of the topics covered in each section and highlight objectives and key concepts. These videos give context to the Narrated Example videos.
• Integrated Review content, which aligns to the Algebra Toolbox, and assessments help you provide students with just the remediation they need, when they need it. Integrated Review consists of:
• Skills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.
• Personalized Skills Review Homework is generated for each student based on the results of the Skills Check Quiz to provide students with help on the prerequisite skills they are lacking. Students receive just the help they need—no more, no less.
• Exercises, Videos, and Worksheets are offered for students who need more help (or for co-requisite courses). There’s no need to go elsewhere for remediation.
• NEW – Personal Assessment Inventories is a collection of online activities designed to promote self-reflection and engagement in students.
• NEW – Mindset videos and assignable, open-ended exercises foster a growth mindset in students.  This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as  learning opportunities — so often a hurdle for math students. 
• NEW – College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course.  Videos can be assigned in a MyLab Math homework assignment to remind students of the crucial content before students begin on their exercises.

Ron Harshbarger received his BS from Shippensburg State and an MST from the University of New Hampshire, did graduate work at Penn State University, and received a PhD from the University of Pittsburgh. During a long and highly successful career at Penn State University, Dr. Harshbarger received both teaching and advising awards. At Georgia Southern University, he taught a wide variety of undergraduate and graduate courses in mathematics, developed five new mathematics courses, and created the mathematics component for a new doctoral degree.

At the University of South Carolina Beaufort, Dr. Harshbarger was named Professor of the Year in 1999. In 2000, Professor Harshbarger was named the Governor’s Professor of the Year for the State of South Carolina. In 2001, the University of South Carolina Board of Trustees named him the Trustee Professor of the Year. In 2002, he received the Mathematical Association of America Southeastern Section Award for Distinguished University Teaching of Mathematics. He was nominated for the 2003 Haimo Award for Distinguished College or University Teaching of Mathematics, a national award given by the Mathematical Association of America. In 2003, he was also named Professor of the Year at the University of South Carolina Beaufort and given the Governor’s Distinguished Professor Award for the state of South Carolina.

Lisa Yocco received her undergraduate degree in mathematics from Augusta State University and her graduate degree in mathematics education from Florida State University. She has taught at both the college level and the high school level for twenty years, with her most recent experience at East Georgia State College. She has co-authored several manuals in mathematics and graphing calculators and has presented workshops and papers at numerous conferences. In addition to her textbook writing and teaching, she enjoys spending time with her three children, cooking, and working on interior decorating.

• More than 250 problems have been replaced with new or updated problems, to keep the real data applications current.
• Preparing for Calculus sections have been added before the Chapter Summaries in Chapters 1 through 6. These sections present approximately 100 problems that use skills from each chapter in calculus contexts, to demonstrate the importance of algebra for those who will be taking calculus.
• Section 3.3 from the previous edition is now divided into two new sections:
• The new Section 3.3 expands coverage of power functions and root functions, and new Section 3.4 expands coverage of piecewise-defined functions and absolute-value functions. 
• These sections have many more examples and exercises than in the 5th Edition.
• Additional modeling problems that involve decision making and critical thinking have been added throughout the text.
• Chapter Toolboxes have been expanded and strengthened to reflect corequisite course content, with more than 80 new exercises. 
• Additional topics include calculations with and properties of real numbers; operations with fractions; evaluating algebraic expressions; solving basic linear equations; evaluating formulas for given values; operations with radicals; rationalizing denominators; operations with complex numbers.
• Specific steps for additional topics have been added to Appendix A.
• More specific Excel steps have been added within the Spreadsheet Solutions in the text, with references to Appendix B for more details. 
• Specific steps for additional topics have been added to Appendix B.
• Discussion of loan amortization using graphing calculators has been added to Chapter 5, and the detailed steps for solving loan amortization problems with graphing calculators have been added to Appendix A.
• Discussion of loan amortization using Excel has been added to Chapter 5, and the detailed steps for solving loan amortization problems with Excel has been added to Appendix B. 
• A Corequisite Notebook by Lisa Yocco is now available to complement this text. It includes all Algebra Toolbox topics with unique exercises for practice, followed by small group activities to enhance classroom time.

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math

• Personal Assessment Inventories is a collection of online activities designed to promote self-reflection and engagement in students.
• Mindset videos and assignable, open-ended exercises foster a growth mindset in students.  This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as  learning opportunities — so often a hurdle for math students. 
• College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course.  Videos can be assigned in a MyLab Math homework assignment to remind students of the crucial content before students begin on their exercises.

Additional information

Dimensions	1.00 × 8.55 × 10.85 in
Imprint	Pearson
Format	gen
ISBN-13	09780135757666
ISBN-10	0135757665
Author	Ronald J. Harshbarger, Lisa S. Yocco
BISAC	SCI055000
Subjects	mathematics, SCI055000, higher education, Precalculus, College Algebra