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Exponential & Logistic Functions

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Exponential & Logistic Functions - PowerPoint PPT Presentation


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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…

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exponential functions
Exponential Functions

f(x)= abx

  • Variable is in the exponent

Growth/Decay

Factor

Principal Amount

(y-intercept)

slide3
Growth

a>0

b>1

Decay

a>0

0

f(x)= 5(1.3)x

f(x)= 5(0.3)x

base e
Base “e”

e = 2.718…

Occurs in many places in “nature”

f(x) = aekx

logistic function
Logistic Function

Growth is RESTRICTED (exponential is unrestricted)

Limit to Growth

“Capacity”

Growth: b < 1

analyze each function
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 function1
Analyze each function

Ex 1)

Ex 2)

  • Limit to growth
  • Horizontal Asymptotes
  • Y-intercept
graph the function y 3 x
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
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
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
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

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