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 `(d V(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) `T^2-1/k` (2) `I-(k T^2)/2` (3) `I-(k(T-t)^2)/2` (4) `e^(-k T)`

Options

A. `T^2 -I/k`
B. `I-(kT^2)/2`
C. `I-(k(T-t)^2)/2`
D. `e^(-kT)`

Answer

B