JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

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

\mathrm{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:

View answer and explanation

Correct option: C

I-\frac{k T^2}{2}

Option C (

I-\frac{k T^2}{2}

) is correct because it represents the scrap value

V(T)

derived from the given differential equation and initial condition.

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