8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.

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Presentation transcript:

8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions in problems involving exponential growth and decay

Example 1: Recognizing Exponential Growth and Decay State whether f(x) is exponential growth or decay Exponential decay 0 < b< 1 Exponential growth b > 1 Exponential decay 0 < b < 1

To see the basic shape of the graph of an exponential decay function: 1. Make a table of values 2. Plot the points.

x

What is the end behavior of the graph?

What is the asymptote? The line y = 0 What is the domain of this function? All real numbers What is the range of this function? y > 0

To graph a general exponential function Graph Then translate graph horizontally by h units to the 2 left and k units up 1

x /2

xx /2-1/2

The domain is all real numbers. The range is y < 1.

Homework: Page 477: #11-17 Odd, #35-41 Odd Table of Values needed for credit

Example 2: Graphing Exponential Functions of the form

x /4

x /3

Plot the points: