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Would you rather have $1 million NOW or 1 penny doubled each day for 30 days?

Would you rather have $1 million NOW or 1 penny doubled each day for 30 days?. Day 30: $5,368,709.12. Exponential & Logistic Functions. Section 3.1.

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Would you rather have $1 million NOW or 1 penny doubled each day for 30 days?

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  1. Would you rather have $1 million NOW or 1 penny doubled each day for 30 days? Day 30: $5,368,709.12

  2. Exponential & Logistic Functions Section 3.1

  3. Objective: determine similarities & difference of exponential & logistic functions; identify asymptotes & intercepts in exponential/logisitc functions • How are exponential & logistic functions alike/different?

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

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

  6. Horizontal Asymptote at y = 0 f(x) = abx y ≠ 0

  7. Base “e” e = 2.718… “the natural number” f(x) = aekx Constant value

  8. How to calculate e

  9. Analyze each function Analyze each function Ex 1) f(x) = 3(2)x Ex 2) f(x) = 2(4)-x+1 • Growth/Decay? • Transformations • End behavior • Y-intercept

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

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

  12. 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

  13. 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

  14. 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

  15. 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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