Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The value $$V(t)$$ depreciates at a rate given by differential equation $$\dfrac{dV(t)}{dt} = -k(T - t)$$, where $$k > 0$$ is a constant and $$T$$ is the total life in years of the equipment. Then the scrap value $$V(T)$$ of the equipment is:

A

$$I - \dfrac{kT^2}{2}$$

B

$$I - \dfrac{k(T-t)^2}{2}$$

C

$$e^{-kT}$$

D

$$T^2 - \dfrac{1}{k}$$