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 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 [AIEEE 2011]

Differential Equations Part 1

Section: Mathematics

Question : 86 of 100

Marks: +1, -0

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)

=−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

[AIEEE 2011]

I−‌
kT2
2
I−‌
k(T−t)2
2
e−kT
T2−‌
1
k

Validate

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