Question

A scientist measures the water temperature in the Gulf at Gulfport on the fifteenth of each month. Her data is shown in the table. What is the average rate of change between March 15 and June 15?

A. 2.6°F per month
B. 3.9°F per month
C. 5.2°F per month
D. 7.8°F per month
Please explain!

Answer 1

C. 5.2°F per month

Explanation:

The average rate of change refers to the relation between these variables.

Specifically, this problem can be modeled by a linear function, where the slope is the average rate of change.

So, such rate can be defined as

`r=(y_(2)-y_(1) )/(x_(2) -x_(1) )`

Where
`(x_(1) ,y_(1) )` is the first pair and
`(x_(2) ,y_(2) )` is the second one.

In this case, the first pair is
`(3,66.8)` and the second pair is
`(6,82.4)`. Replacing these coordinates, we have

`r=(y_(2)-y_(1) )/(x_(2) -x_(1) )=(82.4-66.8)/(6-3)=(15.6)/(3)=5.2`

Which is expressed in Fahrenheit.

Therefore, the average rate of change is 5.2 °F.

This can be interpreted as "The temperature changes +5.2 °F each month between March 15 and June 15".

Answer 2

The average rate of change between March 15 and June 15 will be given by:
(82.4-66.8)/(6-3)
=15.6/3
=5.2° F per month

Answer: C