Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions

3.5 EXPONENTIAL AND LOGARITHMIC MODELS Copyright © Cengage Learning. All rights reserved.

3 Recognize the five most common types of models involving exponential and logarithmic functions. Use exponential growth and decay functions to model and solve real-life problems. Use Gaussian functions to model and solve real-life problems. What You Should Learn

4 Use logistic growth functions to model and solve real-life problems. Use logarithmic functions to model and solve real-life problems. What You Should Learn

5 Introduction

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7 Exponential Growth and Decay

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19 Logistic Growth Models

20 Logistic Growth Models Some populations initially have rapid growth, followed by a declining rate of growth, as indicated by the graph in Figure One model for describing this type of growth pattern is the logistic curve given by the function where y is the population size and x is the time. An example is a bacteria culture that is initially allowed To grow under ideal conditions, and then under less favorable conditions that inhibit growth. A logistic growth curve is also called a sigmoidal curve. Figure 3.40

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22 Logarithmic Models When a Physical quantity varies over a very large range, it is convenient to take its log to have a more manageable set of numbers.

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