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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

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 ) dt =- 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

Options

  1. AI - KT ^2 2
  2. BI - K ( T - t )^2 2
  3. Ce^ -K T
  4. DT ^2- 1 ~K

Correct answer

A. I - KT ^2 2

Step-by-step solution

aligned & d V(t) d t =-K(T-t) & V(t)= K(T-t)^2 2 +C aligned At t = O , V = I C = I - KT ^2 2 Scrap value V ( T ) V ( t = T )= C = I - KT ^2 2

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