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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 `(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)`

A

`T^2 -I/k`

B

`I-(kT^2)/2`

C

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

D

`e^(-kT)`

Text Solution

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The correct Answer is:
B
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