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An equipment has purchase value I, and its worth after t years is V(t). The value falls according to dV/dt = -k(T - t), where k > 0 is constant and T is the equipment's total life in years. Find the scrap value V(T).
- I - k(T - t)²/2
- e^(-kT)
- T² - I/k
- I - kT²/2
Correct answer: I - kT²/2
Solution
Integrating gives V(t) = I - k[Tt - t²/2]; setting t = T yields V(T) = I - kT²/2.
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