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.

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.