You make an initial deposit of $500 in a savings account and plan on making future deposits at a gradually increasing annual rate given by 90t + 810 dollars per year, t years after the initial deposit. Assume that the deposits are made continuously and that interest is compounded continuously at the rate of 6%. Let P(t) denote the amount of money in the account.

(a) Set up an initial-value problem that is satisfied by P(t).

(b) Find P(t).