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 diferential 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

Question

( A ) $e^{-KT}$
( B ) $I-\frac{KT^2}{2}$
( C ) ${T^2}-\frac{1}{K}$
( D ) $I-K{T^2}$