Business Econ: Limits and Continuity

Question

If $900 is invested in an account that pays 3​% compounded​ annually, the total​ amount, A(t), in the account after t years is A(t)=900(1.03)^t

a.) Find the average rate of change per year of the total amount in the account for the first four years of the investment​ (from t=0 to t=4​).

b.) Find the average rate of change per year of the total amount in the account for the second four years of the investment​ (from t=4 to t=8​).

c.) Estimate the instantaneous rate of change for t=4.

(Round to the nearest cent as needed.)

Answer 1

Average Rate of Change = A(t2) - A(t1) / t2-t1

a. [900 (1.03)^4] - [900 (1.03)^0] / 4-0 = 28.24

b. [900 (1.03)^8] - [900 (1.03)^4] / 8-4 = 31.78

c. [900 (1.03)^4.001] - [900 (1.03)^4] / 4.001-4= 29.94