Question

when you own a pet, there are one - time costs, such as a leash, and continuing costs, such as food. suppose the one - time costs for owning a small dog are $180, and the continuing costs are $400 per year
which function models the average annual cost of owning a small dog for x years?
$f(x)=(180 + 400x)/x$
complete
the average annual cost of owning a small dog for 10 years is $418
complete
the function $g(x)=\frac{140 + 500x}{x}$ models the average annual cost of owning a cat for x years. on average, which pet costs more per year over a 10 - year period?
the cat
complete
on average, how much more is the total cost of owning a cat for 10 years than owning a small dog for 10 years? $
done

Explanation:

Step1: Calculate total cost of dog for 10 years

The total cost for the dog is one - time cost plus continuing cost for 10 years. The one - time cost is $180 and the continuing cost per year is $400. So total cost \(C_{dog}=180 + 400\times10=180 + 4000 = 4180\) dollars.

Step2: Calculate total cost of cat for 10 years

First, find the average annual cost of the cat for 10 years using the function \(g(x)=\frac{140 + 500x}{x}\). When \(x = 10\), \(g(10)=\frac{140+500\times10}{10}=\frac{140 + 5000}{10}=\frac{5140}{10}=514\) dollars per year. Then the total cost for the cat for 10 years is \(514\times10 = 5140\) dollars.

Step3: Find the difference in total costs

Subtract the total cost of the dog from the total cost of the cat. \(5140-4180 = 960\) dollars.

Answer:

960