Question

Topic 6: Rate of change Note: A rate of change is a rate that describes how one quantity changes in relation to another. A constant rate of change is the rate of change of a linear relationship. Ex 6: Find the rate of change below AND explain it in words.

Answer 1

Rate of Change

As stated in the question, the rate of change measures how one quantity changes with respect to another.

The question talks about two quantities: The number of hours passed and the number of candies sold. The corresponding data is shown in the table.

Let's call H to the number of hours passed and C to the number of candies sold. We are interested in calculating the changes of C divided by the changes of H as follows:

`r=\frac{\text{change of C}}{change\text{ of H}}`

Take the first two rows of the table. The change of C is 9 - 5 = 4. The change of H is 8 - 7 = 1, thus the rate of change is:

`r=(9-5)/(8-7)=(4)/(1)=4`

This means 4 candies are sold per hour.

Now take the second and the third rows.

`r=(13-9)/(9-8)=(4)/(1)=4`

Again, we get 4 candies per hour.

You can use any pair of rows (including non-continuous rows) and you will get the same result.

Based on those results, we can conclude the rate of change is constant and has a value of 4 candies per hour.