Differential EquationHard
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 
= - k (T - 1), 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
= - k (T - 1), 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 isOptions
A.
B.
C.e-kt
D.
Solution
= - k (T - 1) ⇒ dV = - k(T - t) Integrate
at t = 0 ⇒ V = I
⇒ V(T) = I - 
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