Question

An air conditioner is turned on at 1:00 pm. By 3:30 pm the room temperature had dropped from 82F to 72F. Find the average rate of change of temperature in this room over the period

Answer 1

Given:

From 1:00 pm to 3:30 pm the room temperature had dropped from 82F to 72F.

To find:

The average rate of change of temperature in this room over the period.

Solution:

Time between 1:00 pm to 3:30 pm is 2 hr 30 minutes, i.e., 2.5 hours.

So, change in time is 2.5 hours.

Room temperature had dropped from 82F to 72F.

Change in temperature = 72 F - 82 F

                                        = -10 F

We know that, average rate of change of temperature in this room over the period is

$m=\dfrac{\text{Change in temperature}}{\text{Change in time}}$

$m=\dfrac{-10}{2.5}$

$m=-4$

Therefore, the average rate of change of temperature in this room over the period is -4. It means the temperature is decreasing 4 F per hour.