Exponential & Logistic Functions

1 / 12

# Exponential & Logistic Functions - PowerPoint PPT Presentation

Exponential & Logistic Functions. Section 3.1. Exponential Functions. f (x) = ab x. Variable is in the exponent. Growth/Decay Factor. Principal Amount (y-intercept). Growth a >0 b>1. Decay a >0 0<b < 1. f (x) = 5( 1.3 ) x. f (x) = 5( 0.3 ) x. Base “ e ”. e = 2.718…

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Exponential & Logistic Functions' - kyrene

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Exponential & Logistic Functions

Section 3.1

Exponential Functions

f(x)= abx

• Variable is in the exponent

Growth/Decay

Factor

Principal Amount

(y-intercept)

Growth

a>0

b>1

Decay

a>0

0

f(x)= 5(1.3)x

f(x)= 5(0.3)x

Base “e”

e = 2.718…

Occurs in many places in “nature”

f(x) = aekx

Logistic Function

Growth is RESTRICTED (exponential is unrestricted)

Limit to Growth

“Capacity”

Growth: b < 1

Analyze each function

Analyze each function

Ex 1) f(x) = 3(2)x

Ex 2) f(x) = 2(4)-x+1

• Transformations
• Growth/Decay?
• End behavior
• Y-intercept
Analyze each function

Ex 1)

Ex 2)

• Limit to growth
• Horizontal Asymptotes
• Y-intercept
Graph the function y = 3x
• Determine the Domain, Range, and y-intercept

D: x is any real number

R: y > 0

Y-intercept is at 1

Graph the function y = (0.5)x
• Determine the Domain, Range, and y-intercept

D: x is any real number

R: y > 0

Y-intercept is at 1

Graph the function y = 5(4)x
• Determine the Domain, Range, and y-intercept

D: x is any real number

R: y > 0

Y-intercept is at 5

Graph the function y = -2(3)x
• Determine the Domain, Range, and y-intercept

D: x is any real number

R: y < 0

Y-intercept is at -2