The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $30,303 in 2012. A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay $500 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 3.5%.

(a) Set up a differential equation that is satisfied by the amount f (t) of money owed on the car loan at time t.

(b) How long will it take to pay off the car loan?