If $1000 is invested in an account that pays 3% compounded annually, the total amount, A(t), in the account after t years is
A(t) = 100011.032^t.

(a) Find the average rate of change per year of the total amount in the account for the first five years of the investment (from t = 0 to t = 5).
(b) Find the average rate of change per year of the total amount in the account for the second five years of the investment (from t = 5 to t = 10).
(c) Estimate the instantaneous rate of change for t = 5.