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 $\frac{dV(t)}{dt}=-k(T-t)$, 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:

1. A
   $I-\frac{k{T}^2}{2}$
2. B
   $I-\frac{k(T-t{)}^2}{2}$
3. C
   $I{e}^{-kT}$
4. D
   $T-\frac{k{I}^2}{2}$