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Exponential & Logistic Functions

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 & Logistic Functions

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  1. Exponential & Logistic Functions Section 3.1

  2. Exponential Functions f(x)= abx • Variable is in the exponent Growth/Decay Factor Principal Amount (y-intercept)

  3. Growth a>0 b>1 Decay a>0 0<b< 1 f(x)= 5(1.3)x f(x)= 5(0.3)x

  4. Base “e” e = 2.718… Occurs in many places in “nature” f(x) = aekx

  5. How to calculate e

  6. Logistic Function Growth is RESTRICTED (exponential is unrestricted) Limit to Growth “Capacity” Growth: b < 1

  7. 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

  8. Analyze each function Ex 1) Ex 2) • Limit to growth • Horizontal Asymptotes • Y-intercept

  9. 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

  10. 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

  11. 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

  12. 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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