The future value of$1000aftertyears invested at4%compounded continuously is

f(t) =1000e^0.04tdollars.

(a) Write the rate-of-change function for the value of the investment. (Hint:Letb=e^0.04

and use the rule forf(x) =b^x.)

f'(t) =dollars per year

(b) Calculate the rate of change of the value of the investment after12years. (Round your answer to three decimal places.)

f'(12) = dollars per year