If $1200 is invested in an account that pays 5% compounded annually, the total amount, a(t), in the account after t years is a(t) = 1200(1.05)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.