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Question

Let I be the purchase value of an equipment and v(t) is the value after it has been used for t years. the value v(t) depreciates at a rate dv(t)dt=k(Tt) where k>0 is a constant and T is the total life in years then the scrap value v(T) of the equipment is

A
IkT22
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B
Ik(Tt)22
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C
ekT
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D
T2IT
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Solution

The correct option is A IkT22
Given,
dv(t)dt=k(Tt)
dv(t)=(kT)dt+ktdt
v(t)=kTt+kt22+c
At t=0,c=1
v(t)=kTt+kt22+1
At t=T
v(T)=kT2+kT22+1=112kT2

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