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. `I-(kT^(2))/(2)`
B. `I-(k(T-t^(2)))/(2)`
C. `e^(-kT)`
D. `T^(2)-(1)/(k)`

Answer

A