Question: Money in a bank account grows continuously at an annual rate of r (when the interest rate is 5%, r = 0.05, and so on). Suppose $2000 is put into the account in 2010.
(a) Write a differential equation satisfied by M, the amount of money in the account at time t, measured in years since 2010.
(b) Solve the differential equation.
(c) Sketch the solution until the year 2040 for interest rates of 5% and 10%.