dtdV=−k(T−t)⇒dV=−k(T−t)dt Integrate V=(−2)−k(T−t)2+c⇒V=2k(T−t)2+c at t=0⇒V=I I=2kT+c⇒c=I−2kTT2⇒c=V(T)=I−2kTT2
JEE Main 2011 — Mathematics Calculus
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 dtdV(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
Held on 30 Apr 2011 · Verified 6 Jul 2026.
I−2kT
1−2k(T−t)2
e−kT
T2−k1
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