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 the differential equation $\frac{dV(t)}{dt} = -k(T - t)$,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
  $I - \frac{kT^2}{2}$
• B
  $I - \frac{k(T - t)^2}{2}$
• C
  $e^{-kT}$
• D
  $T^2 - \frac{1}{k}$