Functions and Change

, by Crauder, Bruce; Evans, Benny; Noell, Alan

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ISBN: 9780395911587 | 0395911583
Cover: Hardcover
Copyright: 1/1/1999

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Supplemental Materials

Preface

Prologue

(434)

Typing mathematical expressions

(1)

Rounding

(1)

Scientific notation

(1)

Parentheses and grouping

(1)

Minus signs

(2)

Special numbers π and e

(1)

Chain calculations

(9)

Prologue Summary

(2)

Functions

(54)

Functions given by formulas

(9)

Functions of one variable

(1)

Functions of several variables

(8)

Functions given by tables

(11)

Reading tables of values

(1)

Filling gaps by averaging

(1)

Average rates of change

(2)

Spotting trends

(8)

Functions given by graphs

(17)

Reading graphs

(3)

Concavity and rates of change

(2)

Inflection points

(2)

Drawing a graph

(10)

Functions given by words

(12)

Comparing formulas and words

(3)

Getting formulas from words

(3)

Proportion

(6)

Chapter Summary

(5)

Graphical and Tabular Analysis

(78)

Tables and trends

(15)

Getting tables from formulas

(5)

Optimizing with tables of values

(10)

Graphs

(20)

Hand-drawn graphs from formulas

(1)

Graphing with the calculator

(1)

Tracing the graph

(1)

Choosing a viewing window in practical settings

(5)

Getting limiting values from graphs

(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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Functions and Change

Table of Contents

Supplemental Materials