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

Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc