If $4000 is saved in an account offering a return of 4% compounded continuously, the future value, S, after t years is given by S = 4000e^0.04t
(1) Calculate the value of S when
(a) t = 5 

(b) t = 5.01 and hence estimate the rate of growth at t = 5. Round your answers to two decimal places.
(2) Write down an expression for dS/dt and hence find the exact value of the rate of growth after five years.