1.

Let I be the purchase value of an equipment and V(t) be the value after ithas been used for t years. The value V(t) depreciates at a rate given bydifferential equation `(d V(t)/(dt)=-k(T-t)`, where `k"">""0`is a constant and T is thetotal life in years of the equipment. Then the scrap value V(T) of theequipment is :(1) `T^2-1/k`(2) `I-(k T^2)/2`(3) `I-(k(T-t)^2)/2`(4) `e^(-k T)`A. ` I-(kT^(2))/2`B. `(dy)/(dx) = (x(1+y^(2)))/(y(1+x^(2)))`C. `e^(-kT)`D. `T^(2) -1/k`

Answer» Correct Answer - a
Given , ` (d{V(t)})/(dt) = -k (T-t)`
` :. d{V(t)} = - k (T-t) dt" "` …(i)
when t = 0, then V (t)=I
` int_(0)^(T)d {V(t)} = int_(0)^(T)- k(T-t)dt`
` rArr V (T) - V(0) = k [ (t-T)^(2)/2]_(0)^(T)`
` rArr V(T) -I = k/2 [{(T-T)^(2)-(0-T)^(2)]`
` :. V (T) = I - k/2 T^(2)`


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