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Let I be the purchase value of an equipm...

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(t))/(dt)= -k(T-t)`, where `k gt 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 _______

A

`I-(k(T-t)^(2))/(2)`

B

`e^(-KT)`

C

`T^(2)-(1)/(k)`

D

`I-(kT^(2))/(2)`

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