Let kt denote the capital stock of an economy at time t

Question

Question: Let K(t) denote the capital stock of an economy at time t. Then net investment at time t, denoted by I(t), is given by the rate of increase K(t) of K(t).

(a) If I(t) = 3t² + 2t + 5 (t ≥ 0), what is the total increase in the capital stock during the interval from t = 0 to t = 5?

(b) If K(t₀) = K₀, find an expression for the total increase in the capital stock from time t = t₀ to t = T when the investment function I(t) is as in part (a).