Exponential and Logarithmic Functions 255

10.1 The Nature of Exponential Functions 256

Simple Exponential Function 256 Graphical Form 256 Generalized Exponential Function 257 A Preferred Base 259 Exercise 10,1 260

10.2 Natural Exponential Functions and the Problem of Growth 260

The Number e 260 A n Eamo mic In terprelation of e 262 Interest Compounding and the Function Ae" 262

Instantaneous Rate of Growth 263 Continuous versus Discrete Growth 265 Discounting and Negative Growth 266 Exercise 10,2 267 103 Logarithms 267

The Meaning of Logarithm 267 Common Log and Natural Log 268 Rides of Logarithms 269 An Application 271 Exercise 10.3 272

10.4 Logarithmic Functions 272

Log Functions an d Expon en tia I Functions 2 72 The Graphical Form 273 Base Conversion 274 Exercise 10.4 276

10.5 Derivatives of Exponential and Logarithmic Functions 277

Log-Function Rule 277 Exponential-Function Rule 278 The Rules Generalized 278 The Case of Rase b 280 Higher Derivatives 2HO An Application 281 Exercise HIS 282

10,6 Optimal Timing 282

A Problem of Wine Storage 282 Maximization Conditions 283 A Problem of Timber Cutting 285 Exercise 10.6 286 10 J Further Applications of Exponential and Logarithmic Derivatives 286 Finding the Rate of Growth 286 Rate of Growth of a Combination of Functions 287

Finding the Point Elasticity 288 Exercise i0.7 290

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