Question

craig bought a treadmill for $400. he estimates that the annual costs to maintain the machine will be $36. which rational function yields the average annual cost in dollars of owning the treadmill for x years?
$f(x) = \frac{400x + 36x}{x}$
$f(x) = \frac{400x + 36}{x}$
$f(x) = \frac{400 + 36}{x}$
$f(x) = \frac{400 + 36x}{x}$

Explanation:

Step1: Calculate total cost

The initial cost is $400 (one - time cost). The annual maintenance cost is $36, so for \(x\) years, the total maintenance cost is \(36x\) dollars. The total cost of owning the treadmill for \(x\) years is the sum of the initial cost and the total maintenance cost, which is \(400 + 36x\) dollars.

Step2: Calculate average annual cost

The average annual cost is the total cost divided by the number of years (\(x\)). So the average annual cost function \(f(x)\) is given by \(f(x)=\frac{400 + 36x}{x}\).

Answer:

\(f(x)=\frac{400 + 36x}{x}\) (the first option among the given ones)