Question

the function y = 3.75 + 1.5(x - 1) can be used to determine the cost in dollars of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

Answer 1

We are given

$y=3.75+1.5(x-1)$

where

y is the cost in dollars

x is distance in dollars

now, we can find derivative

$y'=\frac{d}{dx}\left(3.75+1.5\left(x-1\right)\right)$

$=\frac{d}{dx}\left(3.75\right)+\frac{d}{dx}\left(1.5\left(x-1\right)\right)$

$=0+1.5$

so,

$y'=0+1.5$

So,

the rate of change of the cost in dollars with respect to the number of miles is 1.5.........Answer