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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
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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
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To see the basic shape of the graph of an exponential decay function: 1. Make a table of values 2. Plot the points.
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x -3 -2 0 1
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What is the end behavior of the graph?
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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
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To graph a general exponential function Graph Then translate graph horizontally by h units to the 2 left and k units up 1
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x -2-12-6 0-3 1-3/2
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xx-2-12-4-11-6-3-5 0-3-2 1-3/2-1/2
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The domain is all real numbers. The range is y < 1.
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Homework: Page 477: #11-17 Odd, #35-41 Odd Table of Values needed for credit
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Example 2: Graphing Exponential Functions of the form
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x -24812 03 13/4
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x-2-18-6 0-2 1-2/3
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Plot the points:
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