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9780470466445

Explorations in College Algebra

by ; ;
  • ISBN13:

    9780470466445

  • ISBN10:

    0470466448

  • Edition: 5th
  • Format: Paperback
  • Copyright: 2011-02-02
  • Publisher: Wiley
  • View Upgraded Edition

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Summary

Explorations in College Algebra, 5th Edition is designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates readers to grasp abstract ideas by solving real-world problems. The problems lie on a continuum from basic algebraic drills to open-ended, non-routine questions. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in the social, physical, and life sciences. The goal of Explorations in College Algebra, 5th Edition is to prepare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us.

Author Biography

Dr. Linda Kime was formerly a professor at the University of Massachusetts-Boston.

Table of Contents

An Introduction to Data and Functions
Describing Single-Variable Data
Visualizing Single-Variable Data
Numerical Descriptors: What is "Average" Anyway?
An Introduction to Algebra Aerobics
An Introduction to Explore and Extend
Describing Relationships between Two Variables
Visualizing Two-Variable Data
Constructing a "60-Second Summary"
Using Equations to Describe Change
An Introduction to Functions
What is a Function?
Representing Functions: Words, Tables, Graphs and Equations
Input and Output: Independent and Dependent Variables
When is a Relationship Not a Function?
The Language of Functions
Function Notation
Domain and Range
Visualizing Functions
Is There a Maximum or Minimum Value?
When is the Output of the Function Positive, Negative or Zero?
Is the Function Increasing or Decreasing?
Is the Graph Concave Up or Concave Down?
Getting the Big Idea
Chapter Summary
Check Your Understanding
Chapter 1 Review: Putting it all Together
Exploration 1.1 Collecting, Representing, and Analyzing Data
Rates of Change and Linear Function
Average Rates of Change
Describing Change in the U.S. Population over Time
Defining the Average Rate of Change
Limitations of the Average Rate of Change
Change in the Average Rate of Change
The Average Rate of Change is a Slope
Calculating Slopes
Putting a Slant on Data
Slanting the Slope: Choosing Different End Points
Slanting the Data with Words and Graphs
Linear Functions: When Rates of Change are Constant
What if the U.S. Population Had Grown at a Constant Rate?
Real Examples of a Constant Rate of Change
The General Equation for a Linear Function
Visualizing Linear Functions
The Effect of b
The Effect of m
Finding Graphs and Equations of Linear Functions
Finding the Graph
Finding the Equation
Special Cases
Direct Proportionality
Horizontal and Vertical Lines
Parallel and Perpendicular Lines
Breaking the Line: Piecewise Linear Functions
Piecewise Linear Functions
The absolute value function
Step functions
Constructing Linear Models for Data
Fitting a Line to Data: The Kalama Study
Reinitializing the Independent Variable
Interpolation and Extrapolation: Making Predictions
Looking for Links between Education and Earnings: Using Regression Lines
Using U.S. Census Data
Summarizing the Data: Regression Lines
Regression Line: How good a fit?
Interpreting Regression Lines: Correlation vs. Causation
Raising More Questions: Going Deeper
Chapter Summary
Check Your Understanding
Chapter 2 Review: Putting it all Together
Having it Your Way
A Case Study on Education and Earnings
When Lines Meet: Linear Systems
Interpreting Intersection Points: Linear and Non-linear Systems
When Curves Collide: Non-linear Systems
When Lines Meet: Linear System
Visualizing and Solving Linear Systems
Visualizing Linear Systems
Strategies for Solving Linear Systems
Linear Systems in Economics: Supply and Demand
Reading between the Lines: Linear Inequalities
Above and Below the Line
Reading between the Lines
Manipulating Inequalities
Breakeven Points: Regions of Profit or Loss
Systems with Piecewise Linear Functions: Tax Plans
Graduated vs. Flat Income Tax
Comparing the Two Tax Models: Flat vs. Graduated Plans
Chapter Summary
Check Your Understanding
Chapter 3 Review: Putting it all Together
Flat vs. Graduated Income Tax: Who Benefits?
A Comparison of Hybrid and Conventional Automobiles
The Laws of Exponents and Logarithms: Measuring the Universe
The Numbers of Science: Measuring Time and Space
Powers of 10 and the Metric System
Scientific Notation
Positive Integer Exponents
Exponent Rules
Common Errors
Estimating Answers
Zero, Negative and Fractional Exponents
Zero and Negative Exponents
Fractional Exponents
Converting Units
Converting Units within the Metric Systems
Converting between the Metric and English Systems
Using Multiple Conversion Factors
Orders of Magnitude
Comparing Numbers of Widely Differing Sizes
Orders of Magnitude
Graphing Numbers of Widely Differing Sizes: Log Scales
Logarithms Base 10
Finding the Logarithms of Powers of 10
Finding the Logarithm of Any Positive Number
Plotting Numbers on a Logarithmic Scale
Chapter Summary
Check Your Understanding
Chapter 4 Review: Putting it all Together
The Scale and the Tale of the Universe
Growth and Decay: An Introduction to Exponential Functions
Exponential Growth
The Growth of E. coli Bacteria
The General Exponential Growth Function
Doubling Time
Looking at Real Growth Data for E. coli Bacteria
Linear vs. Exponential Functions
General Forms: Linear and Exponential Function
Data Tables: Identifying Linear and Exponential
Finding the Equation for an Exponential Function
Comparing the Average Rates of Change
In the Long Run, Exponential Growth Will Always Outpace Linear Growth
Exponential Decay
The Decay of Iodine-131
The General Exponential Decay Function
Half-Lives
Visualizing Exponential Functions
The Graphs of Exponential Functions
Horizontal Asymptotes
Exponential Functions: A Constant Percent Change
Exponential Growth: Increasing by a Constant Percent
Exponential Decay: Decreasing by a Constant Percent
Revisiting Linear vs. Exponential Functions
More Interesting Examples of Exponential Growth and Decay
Fitting a Curve
Doubling Time and Half-Life: Translating between Forms
The "Rule of 70"
The Malthusian Dilemma
Forming a Fractal Tree
Compound Interest and the Number e
Compounding at Different Intervals
Continuous Compounding Using e
Exponential Functions Base e
Converting ek into a
Semi-log Plots of Exponential Functions
Chapter Summary
Check Your Understanding
Chapter 5 Review: Putting it all Together
Computer Viruses
Logarithmic Links: Logarithmic and Exponential Functions
Using Logarithms to Solve Exponential Equations
Estimating Solutions to Exponential Equations
Rules for Logarithms
Solving Exponential Equations
Solving for Doubling Times and Half-Lives
Using Natural Logarithms to Solve Exponential Equations Base e
The Natural Logarithm
Returning to Doubling Times and Half-Lives
Visualizing and Applying Logarithmic Functions
The Graphs of Logarithmic Functions
Logarithmic Growth
Explore & Extend 6.3: Visualizing Logarithmic Functions
Stretching, Compressing and Reflecting
The Relationship between Logarithmic and Exponential Functions
Logarithmic vs. exponential growth
Logarithmic and exponential functions are inverses of each other
Applications of Logarithmic Functions
Measuring acidity: The pH scale
Using Semi-log Plots to Construct Exponential Models for Data
Why Do Semi-Log Plots of Exponential Functions Produce Straight Lines?
Chapter Summary
Check Your Understanding
Chapter 6 Review: Putting it all Together
Properties of Logarithmic Functions
Power Functions
The Tension between Surface Area and Volume
Scaling Up a Cube
Size and Shape
Direct Proportionality: Power Functions with Positive Powers
Direct Proportionality
Properties of Direct Proportionality
Direct Proportionality with more than one Variable
Visualizing Positive Integer Powers
The Graphs of f(x)=x 2 and g(x)=x 3
Explore & Extend 7.3: Visualizing Power Functions
Odd vs. Even Powers
Symmetry
The Effect of the Coefficient k
Comparing Power and Exponential Functions
Which Eventually Grows Faster, a Power Function or an Exponential Function?
Inverse Proportionality: Power Functions with Negative Integer Powers
Inverse Proportionality
Properties of Inverse Proportionality
Explore & Extend 7.5: Designing Stringed Instruments
Inverse Square Laws
Visualizing Negative Integer Power Functions
The Graphs of f(x)=x^-1 and g(x)=x^-2
Odd vs. Even Powers
Asymptotes
Symmetry
Explore & Extend 7.6: Finding Symmetries
The Effect of the Coefficient k
Using Logarithmic Scales to Find the Best Functional Model
Looking for Lines
Why is a Log-Log Plot of a Power Function a Straight Line?
Translating Power Functions into Equivalent Logarithmic Functions
Analyzing Weight and Height Data
Using a standard plot
Using a semi-log plot
Using a log-log plot
Explore & Extend 7.7: Constructing Functions from Log-Log Plots
Allometry: The Effect of Scale
Chapter Summary
Check Your Understanding
Chapter 7 Review: Putting it all Together
Scaling Objects
Quadratics and the Mathematics of Motion
An Introduction to Quadratic Functions: The Standard Form
The Simplest Quadratic
Designing parabolic devices
The Standard Form of a Quadratic
Properties of Quadratic Functions
Estimating the Vertex and Horizontal Intercepts
Visualizing Quadratics: The Vertex Form
Stretching and Compressing Vertically
Reflections across the Horizontal Axis
Shifting Vertically and Horizontally
Using Transformations to Get the Vertex Form
The Standard Form vs. the Vertex Form
Finding the Vertex from the Standard Form
Converting between Standard and Vertex Forms
Finding the Horizontal Intercepts: The Factored Form
Using Factoring to Find the Horizontal Intercepts
Factoring Quadratics
Using the Quadratic Formula to Find the Horizontal Intercepts
The discriminant
Imaginary and complex numbers
The Factored Form
The Mathematics of Motion
The Scientific Method
Deriving an Equation Relating Distance and Time
Velocity: Change in Distance over Time
Acceleration: Change in Velocity over Time
Deriving an Equation for the Height of an Object in Free Fall
Working with an Initial Upward Velocity
The Average Rate of Change of a Quadratic Function
Chapter Summary
Check Your Understanding
Chapter 8 Review: Putting it all Together
How Fast are You? Using a Ruler to Make a Reaction Timer
New Functions from Old
Transforming a Function
Transformations
Stretching, compressing and shifting
Reflections
Symmetry
Combining Two Functions
The Algebra of Functions
Polynomial Functions
Rational Functions
A Final Example
Chapter Summary
Check Your Understanding
Chapter 9 Review: Putting it all Together
Appendix: Student Data Tables for Exploration 2.1
Data Dictionary for FAM1000 Data
Solutions
Table of Contents provided by Publisher. All Rights Reserved.

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