Questions Asked in Previous 10 Years' Exams Let \( I \) be the purchase value of an equipment an...

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Questions Asked in Previous 10 Years' Exams
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 \( \frac{d V(t)}{d t}=-k(T-t) \), where \( k0 \) is a constant and \( T \) is the total life in years of the equipment. Then, the scrap value \( V(T) \) of the equipment is
[2010 NEEE]
(a) \( I-\frac{k T^{2}}{2} \)
(b) \( I-\frac{k(T-t)^{2}}{2} \)
(c) \( e^{-k T} \)
(d) \( T^{2}-\frac{1}{k} \)
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