Let's determine the average change per hour in temperature between 4:00 AM and 2:00 PM by following these steps.
Step 1: Identify the temperatures recorded at different times
- Temperature at 4:00 AM: [tex]\(-8.4^\circ F\)[/tex]
- Temperature at 8:00 AM: [tex]\(-2.3^\circ F\)[/tex]
- Temperature at 11:00 AM: [tex]\(2.7^\circ F\)[/tex]
- Temperature at 2:00 PM: [tex]\(5.9^\circ F\)[/tex]
Step 2: Determine the total change in temperature
Calculate the change in temperature from 4:00 AM to 2:00 PM. The total change in temperature is the difference between the final temperature (at 2:00 PM) and the initial temperature (at 4:00 AM):
[tex]\[
\text{Total change in temperature} = 5.9^\circ F - (-8.4^\circ F) = 5.9^\circ F + 8.4^\circ F = 14.3^\circ F
\][/tex]
Step 3: Determine the total time interval
Calculate the total time elapsed between 4:00 AM and 2:00 PM:
[tex]\[
\text{Total time interval} = 2:00 \, \text{PM} - 4:00 \, \text{AM} = 10 \, \text{hours}
\][/tex]
Step 4: Calculate the average change per hour
To find the average change per hour, divide the total change in temperature by the total time interval:
[tex]\[
\text{Average change per hour} = \frac{\text{Total change in temperature}}{\text{Total time interval}} = \frac{14.3^\circ F}{10 \, \text{hours}} = 1.43^\circ F/\text{hour}
\][/tex]
Therefore, the average change per hour in temperature between 4:00 AM and 2:00 PM is approximately [tex]\(1.43^\circ F/\text{hour}\)[/tex].
