JEE Math Practice Question

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 $${{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),$$ 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.$$I - {{k{T^2}} \over 2}$$
2. B.$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$
3. C.$${e^{ - kT}}$$
4. D.$${T^2} - {1 \over k}$$