A young person with no initial capital invests k dollars per year in a retirement account at an annual rate of return 0.08. Assume that investments are made continuously and that the return is compounded continuously.


a. Write a differential equation which models the rate of the change of the sum S(t) with t in years (this will involve the parameter k).

b. Use part (a) to determine a formula for the sum S(t) -- (this will involve the parameter k):

S(t)=


c. What value of k will provide 1306000 dollars in 48 years?