Exponential & Logistic Functions Today you will examine exponential functions and identify and graph exponential and logistic functions.
Exponential & Logistic Functions Today you will examine exponential functions and identify and graph exponential and logistic functions.
Dec 14, 2015
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Exponential & Logistic Functions
Today you will examine exponential functions and identify and graph
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
Why?
Exponential and Logistic functions model many growth patterns, including the growth of human and animal populations.
What are Exponential Functions?
Identifying Exponential Functions
Which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not.
-x
4
( ) 3 ( )=7 2
( ) 6 ( ) 5 6
( ) 2 1.5
x
x
f x k x
g x x q x
h x
Finding an Exponential Function from its Table of Values
Determine a formula for the exponential function whose values are given.
Determine a formula for the exponential function whose graph is given.
Summary of Exponential Functions
Transforming Exponential Functions
Describe how to transform the graph of ( ) 2 into
the graph of the given function. Support your answer with
a grapher.
xf x
1( ) 2xg x
Transformation of 12 to 2x x
Transforming Exponential Functions
Describe how to transform the graph of ( ) 2 into
the graph of the given function. Support your answer with
a grapher.
xf x
( ) 2 xh x
Transformation of 2 to 2x x
Transforming Exponential Functions
Describe how to transform the graph of ( ) 2 into
the graph of the given function. Support your answer with
a grapher.
xf x
( ) 3 2xk x
Transformation of 2 to 3 2x x
The Exponential Function
Transforming Exponential Functions
Transforming Exponential Functions
Recap
• How do you tell if a function is exponential?
• How do you determine a formula for an exponential function given a table of values? The graph?
• Describe some characteristics of the graph of an exponential function.
• How do you determine transformations of exponential functions?
Assignment
A 4.10 Sect I
pgs. 286 – 287
#1-6, 11, 13, 19, 23, 39, 40, and 53.
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