Question

The function y = 14 + 2.31x + 4.50 can be used to determine the cost in dollars for an Uber rideof x miles which takes no longer than 10 minutes.What is the rate of change of the cost in dollars with respect to the number of miles?$14 per mileO $2.31 per mileO $4.50 per mileO $6.81 per mile

Answer 1

You have the following function that determines the cost in dollars for an Uber ride in x miles:

`y=14+2.31x+4.50`

In order to determine the rate of change of the costs, with respect to the number of miles, you take into account that the given function can be written as an equation of a line. In fact, the given function can be written as follow:

`\begin{gathered} y=14+2.31x+4.50 \\ y=2.31x+(14+4.50) \\ y=2.31x+18.50 \end{gathered}`

The last equation is the same equation for a line, where the coeffcient in the term with the variable x is the slope of the line, that in this case is 2.31. The slope of the function is precisely the rate of change.

Thus, the rate of hange is 2.31 dollars per mile.