Explorations in College Algebra

by Kime, Linda Almgren; Clark, Judy; Agras, Norma M.

• ISBN13: 9780471106982
• ISBN10: 0471106984
• Edition: CD
• Format: Paperback
• Copyright: 1998-02-01
• Publisher: John Wiley & Sons Inc

Summary

This innovative book, the product of an NSF-funded grant, leads the way in revitalizing college algebra. It offers the fundamentals of college algebra using an approach readers can relate to and use throughout their lifetime. The book contains essays which correlate to the materials to allow for a qualitative understanding of algebra.

Table of Contents

PART I: ALGEBRA IN THE SOCIAL SCIENCES	1	(210)
Exploring Data	3	(40)
CHAPTER 1 MAKING SENSE OF DATA	3	(40)
1.1 An Introduction to Variables and Data	4	(1)
1.2 Reading and Interpreting Data Tables	4	(5)
1.3 Visualizing Data	9	(3)
1.4 What Is Average Anyway?	12	(4)
1.5 Writing About Data	16	(5)
1.6 Does the Whole Process Make Sense?	21	(4)
Chapter Summary	25	(1)
Exercises	26	(9)
Exploration 1.1: Collecting Data	35	(3)
Exploration 1.2: Organizing and Visualizing Data	38	(1)
Exploration 1.3: Describing Data Using Numbers and Graphs	39	(2)
Exploration 1.4: Comparing the Ages of Men and Women in the United States	41	(2)
Exploring Functions	43	(32)
CHAPTER 2 AN INTRODUCTION TO FUNCTIONS	43	(32)
2.1 Relationships Between Two Variables	44	(4)
2.2 Functions	48	(5)
2.3 Equations that Represent Functions	53	(7)
2.4 Fitting Functions to Data	60	(4)
Chapter Summary	64	(1)
Exercises	65	(5)
Exploration 2.1: Picturing Functions	70	(2)
Exploration 2.2: Deducing Formulas to Describe Data	72	(3)
Measuring Change	75	(28)
CHAPTER 3 RATES OF CHANGE	75	(28)
3.1 Average Rates of Change	76	(2)
3.2 A Closer Look at Average Rates of Change	78	(3)
3.3 Generalizing the Concept of the Average Rate of Change	81	(6)
3.4 Other Ways to Describe Change over Time	87	(2)
Chapter Summary	89	(1)
Exercises	90	(9)
Exploration 3.1: Having It Your Way	99	(2)
Exploration 3.2: Why "Average" Rate of Change?	101	(2)
Linear Functions	103	(108)
CHAPTER 4 WHEN RATES OF CHANGE ARE CONSTANT	103	(46)
4.1 A First Look at Linear Relationships	104	(5)
4.2 Linear Functions	109	(4)
4.3 Generating Linear Equations (Three Cases)	113	(6)
4.4 Estimating Linear Models for Data	119	(4)
4.5 Special Cases	123	(11)
4.6 Equivalent Ways of Describing Linear Relationships	134	(2)
Chapter Summary	136	(2)
Exercises	138	(7)
Exploration 4.1 A: Looking at Lines	145	(2)
Exploration 4.1 B: Looking at Lines with a Graphing Calculator	147	(2)
CHAPTER 5 LOOKING FOR LINKS: A CASE STUDY IN EDUCATION AND INCOME	149	(30)
5.1 A Case Study Using U.S. Census Data	150	(3)
5.2 Summarizing the Data: Regression Lines	153	(5)
5.3 Correlation Versus Causation	158	(2)
5.4 Next Steps: Raising More Questions	160	(3)
Chapter Summary	163	(1)
Exercises	164	(11)
Exploration 5.1: A Case Study on Education and Income in the United States: Part I	175	(2)
Exploration 5.2: A Case Study on Education and Income in the United States: Part II	177	(2)
CHAPTER 6 WHEN LINES MEET	179	(32)
6.1 An Economic Comparison of Solar Versus Conventional Heating Systems	180	(3)
6.2 Finding Solutions to Systems of Linear Equations	183	(7)
6.3 Intersection Points Representing Equilibrium	190	(2)
6.4 Graduated Versus Flat Income Tax: Using Piecewise Linear Functions	192	(7)
Chapter Summary	199	(1)
Exercises	200	(8)
Exploration 6.1: Flat Versus Graduated Income Tax: Who Benefits?	208	(3)
PART II: ALGEBRA IN THE PHYSICAL AND LIFE SCIENCES	211	(279)
Using Powers	213	(50)
CHAPTER 7 DEEP TIME AND DEEP SPACE	213	(50)
7.1 Powers of Ten	214	(5)
7.2 Scientific Notation	219	(2)
7.3 Expressions of the Form a(n)	221	(8)
7.4 Converting Units	229	(3)
7.5 Expressions of the Form a(m/n)	232	(6)
7.6 Orders of Magnitude	238	(4)
7.7 Logarithms Base 10	242	(6)
Chapter Summary	248	(2)
Exercises	250	(9)
Exploration 7.1: The Scale and the Tale of the Universe	259	(2)
Exploration 7.2: Patterns in the Position and Motion of the Planets	261	(2)
Exponential Functions	263	(46)
CHAPTER 8 GROWTH AND DECAY	263	(46)
8.1 Modeling Growth	264	(7)
8.2 Visualizing Exponential Functions	271	(3)
8.3 Exponential Growth or Decay Expressed in Percentages	274	(2)
8.4 Examples of Exponential Growth and Decay	276	(13)
8.5 Semi-log Plots of Exponential Functions	289	(2)
Chapter Summary	291	(1)
Exercises	292	(9)
Exploration 8.1: Devising a Model for the Growth of Bacteria	301	(4)
Exploration 8.2: Properties of Exponential Functions	305	(2)
Exploration 8.3: Recognizing Exponential Patterns in Data Tables	307	(2)
Power Functions	309	(44)
CHAPTER 9 FUNCTIONING WITH POWERS	309	(44)
9.1 The Tension between Surface Area and Volume	310	(4)
9.2 Power Functions with Positive Powers	314	(6)
9.3 Visualizing Positive Integer Powers	320	(4)
9.4 Comparing Power and Exponential Functions	324	(2)
9.5 Polynomials: Combining Positive Integer Power Functions	326	(2)
9.6 Power Functions with Negative Integer Powers	328	(9)
9.7 Visualizing Negative Integer Power Functions	337	(1)
Chapter Summary	338	(2)
Exercises	340	(7)
Exploration 9.1: Predicting Properties of Power Functions	347	(2)
Exploration 9.2: Scaling Objects	349	(2)
Exploration 9.3: Visualizing Power Functions with Negative Integer Powers	351	(2)
Quadratic and Other Polynomial Functions	353	(84)
CHAPTER 10 THE MATHEMATICS OF MOTION: A CASE STUDY	353	(28)
10.1 The Scientific Method	354	(1)
10.2 Interpreting Data from a Free-Fall Experiment	354	(3)
10.3 Deriving an Equation Relating Distance and Time	357	(2)
10.4 Deriving Equations for Velocity and Acceleration	359	(4)
10.5 Using the Free-Fall Equations	363	(5)
Chapter Summary	368	(1)
Exercises	369	(6)
Exploration 10.1: Free-Fall Experiment	375	(4)
Exploration 10.2: Constructing Equations of Motion	379	(2)
CHAPTER 11 PARABOLIC REFLECTIONS AND POLYNOMIALS	381	(56)
11.1 Visualizing Quadratic Functions	382	(4)
11.2 Finding the Vertex	386	(3)
11.3 Finding the Intercepts	389	(7)
11.4 Different Forms of the Quadratic Function	396	(1)
11.5 The Factored Form of the Quadratic Function	397	(4)
11.6 Lifts and Shifts: Understanding the a-h-k Form	401	(6)
11.7 Why the Formula for the Vertex and the Quadratic Formula Work	407	(3)
11.8 Generalizing to Other Polynomials	410	(7)
Chapter Summary	417	(2)
Exercises	419	(10)
Exploration 11.1: Properties of Quadratic Functions	429	(3)
Exploration 11.2: Getting to the Root of Things	432	(3)
Exploration 11.3: Constructing Under Constraints	435	(2)
Logarithmic Functions	437	(53)
CHAPTER 12 LOGARITHMIC LINKS: LOGARITHMIC, EXPONENTIAL AND POWER FUNCTIONS	437	(53)
12.1 Using Logarithms to Solve Exponential Equations	438	(9)
12.2 Base e	447	(5)
12.3 The Natural Logarithm	452	(3)
12.4 Logarithmic Functions	455	(5)
12.5 Writing Exponential Functions Using Base e	460	(4)
12.6 Using Logarithmic Scales to Find the Best Function Model	464	(8)
12.7 Allometry: The Effect of Scale	472	(3)
Chapter Summary	475	(3)
Exercises	478	(7)
Exploration 12.1: Properties of Logarithmic Functions	485	(3)
Exploration 12.2: Revisiting the U.S. Population Data	488	(2)
APPENDICES	490	(151)
Anthology of Readings	490	(107)
Answers to Algebra Aerobics	597	(22)
Brief Solutions to Odd-Numbered Problems	619	(22)
Index	641