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{400 + 36x}{x} \\) \\( f(x) = \frac{400x + 36}{x} \\) \\( f(x) = \frac{400 + 36}{x} \\) \\( f(x) = \frac{400 + 36x}{x} \\) (note: some function expressions may have typographical repetitions in the original, but the key context is about finding the rational function for average annual cost.)

Explanation:

Step1: Determine total cost

The initial cost is $400, and the annual maintenance cost is $36. For \( x \) years, the total maintenance cost is \( 36x \). So the total cost over \( x \) years is \( 400 + 36x \).

Step2: Calculate average annual cost

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

Answer:

\( f(x)=\frac{400 + 36x}{x} \) (assuming the first option with \( f(x)=\frac{400 + 36x}{x} \) is the correct one among the given choices)