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Differential Equations question

2011 · Shift 0 · Q38

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JEE Main
Mathematics
Differential Equations
2011 · Shift 0 · Q38

Differential Equations question

2011 · Shift 0 · Q38

JEE MainMathematicsDifferential EquationsMCQ+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

{{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),

where

k\gt 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

A
$I - {{k{T^2}} \over 2}$
B
$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$
C
${e^{ - kT}}$
D
${T^2} - {1 \over k}$

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