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Chapter 3. Exponential, Logistic, and Logarithmic Functions. 3.1. Exponential and Logistic Functions. Quick Review. Quick Review Solutions. What you’ll learn about. Exponential Functions and Their Graphs The Natural Base e Logistic Functions and Their Graphs Population Models … and why
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Chapter 3 Exponential, Logistic, and Logarithmic Functions
3.1 Exponential and Logistic Functions
What you’ll learn about • Exponential Functions and Their Graphs • The Natural Base e • Logistic Functions and Their Graphs • Population Models … and why Exponential and logistic functions model many growth patterns, including the growth of human and animal populations.
Example Finding an Exponential Function from its Table of Values
Example Finding an Exponential Function from its Table of Values
3.2 Exponential and Logistic Modeling
What you’ll learn about • Constant Percentage Rate and Exponential Functions • Exponential Growth and Decay Models • Using Regression to Model Population • Other Logistic Models … and why Exponential functions model many types of unrestricted growth; logistic functions model restricted growth, including the spread of disease and the spread of rumors.
Constant Percentage Rate Suppose that a population is changing at a constant percentage rate r, where r is the percent rate of change expressed in decimal form. Then the population follows the pattern shown.
Example Finding an Exponential Function Determine the exponential function with initial value=10, increasing at a rate of 5% per year.
Example Finding an Exponential Function Determine the exponential function with initial value=10, increasing at a rate of 5% per year.
Example Modeling U.S. Population Using Exponential Regression Use the 1900-2000 data and exponential regression to predict the U.S. population for 2003.
Example Modeling U.S. Population Using Exponential Regression Use the 1900-2000 data and exponential regression to predict the U.S. population for 2003.
Maximum Sustainable Population Exponential growth is unrestricted, but population growth often is not. For many populations, the growth begins exponentially, but eventually slows and approaches a limit to growth called the maximum sustainable population.
3.3 Logarithmic Functions and Their Graphs
What you’ll learn about • Inverses of Exponential Functions • Common Logarithms – Base 10 • Natural Logarithms – Base e • Graphs of Logarithmic Functions • Measuring Sound Using Decibels … and why Logarithmic functions are used in many applications, including the measurement of the relative intensity of sounds.
Common Logarithm – Base 10 • Logarithms with base 10 are called common logarithms. • The common logarithm log10x = log x. • The common logarithm is the inverse of the exponential function y = 10x.
