Question

The cost of a machine depreciates every year and can be modeled using the function  C (x ) = 800(0.95) x, where C (x ) is the cost of the machine, in dollars, x years after it was bought. The owner of the machine claims that the cost of the machine decreases by $40 every year. Is the claim correct? Explain.

Answer 1

Given that the model for machine depreciation is:
C(x)=800(0.95)^x
to evaluate the amount in cash that the machine depreciates at we let x=1, this will represent 1 year that we want to determine. Thus we shall have:
C(1)=800(0.95)^1
C(1)=$760
thus the amount of depreciation is:
800-760
=$40
Therefore we conclude that the machine depreciates at $40 per year. The claim is correct.