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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, 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.

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

- 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.

a.

b.

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