Question

The average cost (in dollars) per mile for riding x miles in a cab is c(x)=2.5+2x/x. As x gets larger and larger, what does the end behavior of the function tell you about the situation?

Answer 1

The average cost per mile decreases

Explanation:

We have the following function:

`C\mleft(x\mright)=(2.5+2x)/(x)`

If we give value to x, we obtain the following:

`\begin{gathered} c(10)=(2.5+2\cdot10)/(10)=2.25 \\ c(50)=(2.5+2\cdot50)/(50)=2.05 \\ c(100)=(2.5+2\cdot100)/(100)=2.025 \\ c(200)=(2.5+2\cdot200)/(200)=2.0125 \end{gathered}`

We can see that it is evident that as x increases, c (x) decreases. Depending on the situation, if we travel more miles, the average cost per mile decreases.