After depositing an initial amount of $10,000 in a savings account that earns 4% interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 - 500t dollars per year, t years from the time the account was opened.

(a) How many years did the person contribute to the account before starting to withdraw money from it?

(b) Let P(t) denote the amount of money in the account, t years after the initial deposit. Find an initial-value problem satisfied by P(t). (Assume that the deposits and withdrawals were made continuously.)