A person deposits $10,000 in a bank account and decides to make additional deposits at the rate of A dollars per year. The bank compounds interest continuously at the annual rate of 6%, and the deposits are made continuously into the account.

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

(b) Determine f (t) (as a function of A). 

(c) Determine A if the initial deposit is to double in 5 years.