Chapter 12 Exponential and Logarithmic Functions

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Chapter 12 Exponential and Logarithmic Functions

• Section 1 Exponential Functions

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Exponential Functions

• These functions model rapid growth or decay
• of users on the Internet
• 16 million (1995) ? 957 million (late 2005)
• Compound interest
• Population growth or decline

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Comparison

• Linear Functions
• Rate of change is constant
• Exponential Functions
• Change at a constant percent rate.

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The Exponential Function

• y abx

• b is the base
• It must be greater than 0
• It cannot equal 1.
• x can be any real number

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Identify Exponential Functions

• Which of the following are exponential functions?

y 3x
y x3
no
yes
y 2(7)x
y 2(-7)x
yes
no
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Identify the Base

• Identify the base in each of the following.

y 3x
y 2(7)x
y 4x - 3
y 3ax
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Evaluate Exponential Functions
y 3x for x 4
y 2(7)x for x 3
y -2(4x) for x 3/2
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Graph Exponential Functions (b gt 1)

• Graph y 2x for x -3 to 3

y
x
-3 -2 -1 0 1 2 3
1/8 1/4 1/2 1 2 4 8
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Graph Exponential Functions (0lt b lt 1)

• Graph y (1/2)x for x -3 to 3

y
x
-3 -2 -1 0 1 2 3
8 4 2 1 1/2 1/4 1/8
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Summary

• y abx

• x can be any value
• The resulting y value will always be positive.
• The y-intercept is always (0,1)
• When b gt 1, as x increases, y increases.
• When 0 lt b lt 1, as x increases, y decreases.

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Practice

• Using Microsoft Excel
• Graph the function y 3x for x -3 to 3 (in
  0.5 increments)
• Graph the function y (1/3)x for x -3 to 3
  (in 0.5 increments)

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Practice Graph using Excel

• Result

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Practice

• MathXL Ch 12 Section 1