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 0 is a constant and T is t

Question

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 >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

Quantrex Academy · Accepted Answer

Correct answer: A. I - kT 2

d V d t =-k(T-t) d V=-k(T-t) d t Integrate V= -k(T-t)^2 (-2) +c V= k(T-t)^2 2 +c at t = 0 V = I I = kT 2 + c c = I - kT T ^2 2 c = V ( T )= I - kT T ^2 2

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