A person deposits an inheritance of $100,000 in a savings account that earns 4% interest compounded continuously. This person intends to make withdrawals that will increase gradually in size with time. Suppose that the annual rate of withdrawals is 2000 + 500t dollars per year, t years from the time the account was opened.

(a) Assume that the withdrawals are made at a continuous rate. Set up a differential equation that is satisfied by the amount f (t) in the account at time t.

(b) Determine f (t).

(c) With the help of your calculator, plot f (t) and approximate the time it will take before the account is depleted.