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**1. Homework Statement**

If you invest $5000 in a stock that is increasing in value at the rate of 12% per year, then the value of your stock is given by:

f(x) = 5000(1.12)^x, where x is measured in years

a) find average value from x = 2 to x = 3

b) find instantaneous value at x = 3

**2. Homework Equations**

y = b^x

y' = (b^x)(ln^x)

**3. The Attempt at a Solution**

a) f(x) = 5000(1.12)^{5 - 2} = 5000(1.12)^3 = 7024.64

b) f'(x) = (5000(1.12)^3)(ln 1.12) = (7024.64)(0.113) = 796.093