Question

Carla is renting a canoe. It costs $80 for 2 hours and $110 for 4 hours. What is the rate of change for this situation?

Answer 1

$15 per hour

Explanation:

The rate of change in this scenario can also be thought of as the slope. After all, the slope of a line also represents the rate of change.

In this problem, we are, in a way, given two coordinate points where the x-coordinate (or the independent variable) is the time and the y-coordinate (or the dependent variable) is the price. This is because the amount of price that Carla will pay depends on the time.

• The first coordinate that we are given is that for 2 hours, it costs $80, which can be represented as `(2,$80)`.

• The second coordinate that we are given is that for 4 hours, it costs $110, which can be represented as `(4, $110)`.

The formula to find the slope with two given coordinates is:
`(y_2 - y_1)/(x_2 - x_1)`

Plug in (substitute) the corresponding numbers into its appropriate places and evaluate .
`(110-80)/(4-2) = 30/2 = 15`

So our answer is $15 per hour.