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7 Jan 2022
Given information
Given a manufacturing company owns a major piece of equipment that depreciates at the (continuous) rate , where is the time measured in months since its last overhaul.
Step-by-step explanation
Step 1.
Let be the value of the equipment at time .
We know from the given information that the rate of depreciation of the equipment is .
Because the derivative gives us the rate of change of a function, we can say that
By taking the integral of both sides and applying the Fundamental Theorem of Calculus, we find that
Because we defined as the value of the equipment, this equation tells us that the integral gives us the total loss of value at time .