An investment account pays 4 percent interest, compounded continuously, and has a balance of $2000 at time t= 0. Lump sum deposits of A dollars are to be made at times t = 2 and t = 4, where A is to be determined. (a) Formulate an appropriate ODE and initial condition. (b) Solve the ODE in part (a). The solution should contain the parameter A. (c) Suppose we want to choose these deposits so the account has $10,000 at time t = 10. What value of A gives the desired account balance?