
College Algebra: Modeling Our World CDRom ( Teachers Edition )
Nancy Crisler, Gary Froelich, Jerry Lege

Mathematics Topic: Algebra, Modeling, Precalculus 
Application Areas: Various 

Click here to view the Student Edition.
To the Teacher
Since its inception in 1980, COMAP has been dedicated to presenting mathematics through
contemporary applications. We have produced high school and college texts, hundreds of
supplemental modules, and three television courses—all with the purpose of showing
students how mathematics is used in their daily lives. College Algebra: Modeling Our World is
a text rooted in the COMAP philosophy.
The word "modeling" is the key. Real problems do not come at the end of chapters. Real problems
don't look like mathematics problems. Real problems are messy. Real problems ask questions such as:
How do we create computer animation? How do we effectively control an animal population? What
is the best location for a fire station? What do we mean by "best"?
Mathematical modeling is the process of looking at a situation, formulating a problem, finding a
mathematical core, working within that core, and coming back to see what mathematics tells us about
the original problem. We do not know in advance what mathematics to apply. The mathematics we
settle on may be a mix of geometry, algebra, trigonometry, data analysis, and probability. We may
need to use computers or graphing calculators, spreadsheets, or other utilities. At heart, we want to
demonstrate to students that mathematics is the most useful subject they will learn. More importantly,
we hope to demonstrate that using mathematics to solve interesting problems about how our world
works can be a truly enjoyable and rewarding experience. Ultimately, learning to model is learning
to learn.
Yes, the text makes extensive use of technology. Yes, the text is activitybased. And, of course, the text
is applications and modeling driven. But, make no mistake. This is a serious precalculus text. We
emphasize that mathematics as a discipline has a structure of its own, and that as students go on into
the study of mathematics they will learn more and more of that structure and the power it provides to
solve an amazingly wide array of problems.
This course is the gateway to collegiate mathematics. As such, students will see a number of essential
new concepts and be asked to learn a number of important new skills And we believe that the
material in this text can provide students with a firm background for any entrylevel undergraduate
mathematics course—continuous or discrete. For example, we have provided substantial material on
matrices and vectors as well as a full chapter on discrete dynamical systems. We believe that the
treatment of these topics will prepare students for a deeper understanding of the concepts underlying
the calculus as well as those underlying discrete mathematical structures.
What you will find here is a challenging precalculus course. And, in the COMAP tradition, you will
find exciting, contemporary applications and models presented in novel ways to help teach and
motivate the further study of our discipline.
Solomon Garfunkel
EXECUTIVE DIRECTOR, COMAP
Table of Contents:
CHAPTER 1
Functions in Modeling
LESSON 1.1:
Functions as Models
LESSON 1.2:
Creating a Mathematical Model
LESSON 1.3:
Modeling Linear Patterns: Beginning the Tool Kit of Functions
LESSON 1.4:
Expanding the Tool Kit of Functions
LESSON 1.5:
Transformations of Functions
LESSON 1.6:
Operations on Functions
CHAPTER 1 REVIEW
CHAPTER 2
The Exponential and Logarithmic Functions
LESSON 2.1: Exponential Functions
LESSON 2.2: Logarithmic Scale
LESSON 2.3: Changing Bases
LESSON 2.4: Logarithmic Functions
LESSON 2.5: Modeling with Exponential and Logarithmic Functions
LESSON 2.6: Composition and Inverses of Functions
CHAPTER 2 REVIEW
CHAPTER 3
Polynomial Models
LESSON 3.1: Modeling Falling Objects
LESSON 3.2: The Merits of Polynomial Models
LESSON 3.3: The Power of Polynomials
LESSON 3.4: Zeroing in on Polynomials
LESSON 3.5: Polynomial Divisions
LESSON 3.6: Polynomial Approximations
CHAPTER 3 REVIEW
CHAPTER 4
Matrices
LESSON 4.1: Matrix Basics
LESSON 4.2: The Multiplicative Inverse
LESSON 4.3: Systems of Equations in Three Variables
CHAPTER 4 REVIEW
CHAPTER 5
Analytic Geometry
LESSON 5.1: Analytic Geometry and Loci
LESSON 5.2: Modeling with Circles
LESSON 5.3: Modeling with Parabolas
LESSON 5.4: Modeling with Ellipses
LESSON 5.5: Modeling with Hyperbolas
CHAPTER 5 REVIEW
CHAPTER 6
Counting and the Binomial Theorem
LESSON 6.1: Counting Basics
LESSON 6.2: Compound Events
LESSON 6.3: The Binomial Theorem
CHAPTER 6 REVIEW
APPENDICES A–H
APPENDICES SOLUTIONS
CALCULATOR APPENDICES A–K
SELECTED SOLUTIONS
INDEX
Teacher’s Guide
Teacher’s Resources
Handouts
Assessment Problems
Transparencies
Software
Solutions Manual
Supplemental Activities
