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3.5 Exponential and Logarithmic Models

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.

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3.5 Exponential and Logarithmic Models

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  1. 3.5 Exponential and Logarithmic Models n compoundings per yearContinuous 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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