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 dt dV ( t ) = − k ( T

Question

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 dt 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

TestHub · Accepted Answer

d t d V ​ = − k ( T − t ) ⇒ d V = − k ( T − t ) d t Integrate V = ( − 2 ) − k ( T − t ) 2 ​ + c ⇒ V = 2 k ( T − t ) 2 ​ + c at t = 0 ⇒ V = I I = 2 kT ​ + c ⇒ c = I − 2 kT T 2 ​ ⇒ c = V ( T ) = I − 2 kT T 2 ​

Mathematics - Differential Equation Question with Solution | TestHub

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