Exponential & Logistic Functions Today you will examine exponential functions and identify and graph...

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




a grapher.

xf x

( ) 2 xh x

Transformation of 2 to 2x x




a grapher.

xf x

( ) 3 2xk x

Transformation of 2 to 3 2x x

The Exponential Function

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.

Exponential & Logistic Functions Today you will examine exponential functions and identify and graph...

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