Aperson borrows $10,000 and repays the loan at the rate of $2,400 per year. the lender charges interest of 10% per year. assuming the payments are made continuously and interest is compounded continuously (a pretty good approximation to reality for long-term loans), the amount m(t) of money (in dollars) owed t years after the loan is made satisfies the differential equationdmdt = 110 m − 2400and the initial conditionm(0) = 1.(a) solve this initial-value problem for m(t).m(t) = (b) how long does it take to pay off the loan? that is, at what time t is m(t) = 0? give your answer (in years) in decimal form with at least 3 decimal digits. years