9780395911587

Functions and Change

by ; ;
  • ISBN13:

    9780395911587

  • ISBN10:

    0395911583

  • Format: Hardcover
  • Copyright: 1999-01-01
  • Publisher: Cengage Learning

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Supplemental Materials

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Table of Contents

Preface xi
Prologue 1(434)
Typing mathematical expressions
1(1)
Rounding
2(1)
Scientific notation
3(1)
Parentheses and grouping
4(1)
Minus signs
5(2)
Special numbers π and e
7(1)
Chain calculations
8(9)
Prologue Summary
15(2)
Functions
17(54)
Functions given by formulas
17(9)
Functions of one variable
17(1)
Functions of several variables
18(8)
Functions given by tables
26(11)
Reading tables of values
26(1)
Filling gaps by averaging
26(1)
Average rates of change
27(2)
Spotting trends
29(8)
Functions given by graphs
37(17)
Reading graphs
37(3)
Concavity and rates of change
40(2)
Inflection points
42(2)
Drawing a graph
44(10)
Functions given by words
54(12)
Comparing formulas and words
54(3)
Getting formulas from words
57(3)
Proportion
60(6)
Chapter Summary
66(5)
Graphical and Tabular Analysis
71(78)
Tables and trends
71(15)
Getting tables from formulas
71(5)
Optimizing with tables of values
76(10)
Graphs
86(20)
Hand-drawn graphs from formulas
86(1)
Graphing with the calculator
86(1)
Tracing the graph
87(1)
Choosing a viewing window in practical settings
88(5)
Getting limiting values from graphs
93(13)
Solving linear equations
106(13)
The basic operations
106(2)
Reversing the roles of variables
108(11)
Solving nonlinear equations
119(13)
The crossing graphs method
119(1)
The single graph method
120(12)
Optimization
132(13)
Optimizing at peaks and valleys
132(4)
Optimizing at endpoints
136(9)
Chapter Summary
145(4)
Straight Lines and Linear Functions
149(60)
The geometry of lines
149(9)
Characterizations of straight lines
149(2)
The slope of a line
151(1)
Getting slope from points
152(6)
Linear functions
158(13)
Constant rates of change
158(2)
Linear functions and straight lines
160(3)
Linear equations from data
163(8)
Modeling data with linear functions
171(13)
Testing data for linearity
171(1)
Linear models
172(3)
Graphing discrete data
175(9)
Linear regression
184(12)
The regression line
184(2)
Uses of the regression line: slope and trends
186(10)
Systems of equations
196(9)
Graphical solutions of systems of equations
196(4)
Algebraic solutions
200(5)
Chapter Summary
205(4)
Exponential Functions
209(56)
Exponential growth and decay
209(14)
Exponential growth
209(1)
Exponential decay
210(3)
Constant proportional change
213(3)
Unit conversion
216(2)
Exponential functions and daily experience
218(5)
Modeling exponential data
223(12)
Recognizing exponential data
223(1)
Constructing an exponential model
224(3)
Growth and decay factor units in exponential modeling
227(8)
Modeling nearly exponential data
235(16)
From linear to exponential data
235(2)
From exponential to linear data: the logarithm
237(2)
Exponential regression
239(6)
A note about the growth rate
245(6)
Another look at exponential regression
251(10)
How a change in In x affects x
251(2)
Continuous compounding and the APR
253(2)
Exponential growth rate and an alternative form
255(6)
Chapter Summary
261(4)
A Survey of Other Common Functions
265(60)
Power functions
265(13)
Homogeneity property of power functions
267(4)
Comparing exponential and power functions
271(7)
Modeling data with power functions
278(19)
The connection between power data and linear data
278(1)
Getting a power model from data
279(4)
Almost power data
283(4)
Graphing on a logarithmic scale: common versus natural logarithms
287(10)
Periodic functions and right triangle trigonometry
297(10)
Period and amplitude
297(2)
Using the sine function to model periodic phenomena
299(2)
Surveying and right triangles
301(6)
Polynomial and rational functions
307(14)
Quadratics and parabolas
307(3)
Linear rates of change and second-order differences
310(5)
The quadratic formula
315(1)
Higher-degree polynomials and their roots
316(1)
Rational functions
317(4)
Chapter Summary
321(4)
Rates of Change
325(68)
Velocity
325(15)
Getting velocity from directed distance
325(2)
Constant velocity means linear directed distance
327(7)
When distance is given by a formula
334(6)
Rates of change for other functions
340(12)
Examples of rates of change
340(1)
Common properties of all rates of change
341(2)
When the rate of change is zero
343(2)
When the rate of change is constant
345(7)
Equations of change: liner and exponential functions
352(10)
Equation of change for linear functions
352(2)
Instantaneous rates of change
354(1)
Equation of change for exponential functions
354(4)
Why equations of change?
358(4)
Equations of change: graphical solutions
362(16)
Equilibrium solutions
362(4)
Sketching graphs
366(12)
Estimating rates of change
378(10)
Rates of change for tabulated data
378(3)
Rates of change for functions given by formulas
381(7)
Chapter Summary
388(5)
Mathematics of Population Ecology
393(42)
Population dynamics: exponential growth
393(12)
Exponential growth
394(2)
Doubling times
396(1)
Empirical data
397(2)
Discrete generations
399(6)
Population dynamics: logistic growth
405(14)
Logistic growth model
405(1)
Application to harvesting renewable resources
406(2)
Logistic equations of change
408(3)
Integral form of the logistic equation
411(2)
The value of the logistic model
413(6)
Population structure: survivorship curves
419(13)
Life tables and survivorship curves
419(1)
Classifying survivorship curves
420(5)
Usefulness of survivorship curves
425(7)
Chapter Summary
432(3)
Brief Answers to Odd-Numbered Exercises 435(22)
Index 457

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