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Exponential and

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3.5 Exponential and Logarithmic Models n compoundings per year Continuous Compounding An investment is made in a trust fund at an annual percentage rate of 9.5% ... – PowerPoint PPT presentation

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Title: Exponential and


1
3.5 Exponential and Logarithmic Models
n compoundings per year Continuous Compounding
2
An investment is made in a trust fund at an
annual percentage rate of 9.5, compounded
quarterly. How long will it take for the
investment to double in value?
Divide by P
Take the ln of both sides.
Move the 4t out front.
3
Do the same example using compounding
continuously.
2P Pe.095t
Time to Double for Continuous Compounding
2 e.095t
ln 2 .095t
Rate needed to Double for Continuous Compounding
4
  • Carbon 14 C14 has a half-life of 5,730
    years. If we
  • start with 3 grams. How many grams are left
    after
  • 1,000 years
  • 10,000 years

Decay and Growth are modeled after the
equation A Cekt
C the initial amount k rate of growth or
decay t time
First, we need to find our rate k.
Note it takes 5,730 years for 1 g to become a
half a g.
5
a.
b.
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