Money in a bank account grows continuously at an annual rate of r (assume r is the interest rate in decimal form). (a) Write a differential equation satisfied by M, the amount of money in the account at time I, measured in years since 2010. d_M=rt 111' x (b) Solve the initial value problem if $4000 is put into an account in 2010. Your answer will still have r in it. M(t) = 5. [-18 Points] The rate at which ice forms on a lake is inversely proportional to the thickness of the ice. Suppose the ice is 3 inches thick when t = 0 and 4 inches thick when t = 7 days. (a) Which of the following can be used to model the thickness of the ice, 1(t)? Assume k > 0. O%=k1 O%= (b) So ve the differential equation. 1(1\") = (c) Assuming the model holds, when will the ice be 4.5 inches thick? Round your answer to two decimal places. days