A company wishes to set aside funds for future expansion and so arranges to make continuous deposits into a savings account at the rate of $10,000 per year. The savings account earns 5% interest compounded continuously.

(a) Set up the differential equation that is satisfied by the amount f (t) of money in the account at time t.

(b) Solve the differential equation in part (a), assuming that f (0) = 0, and determine how much money will be in the account at the end of 5 years.