To determine the average change per hour in temperature between 4:00 AM and 2:00 PM, let's follow these steps:
1. Identify the temperature at the start and end times:
- At 4:00 AM, the temperature was [tex]\(-8.4^\circ F\)[/tex].
- At 2:00 PM, the temperature was [tex]\(5.9^\circ F\)[/tex].
2. Calculate the total change in temperature:
- The formula to calculate the change in temperature is:
[tex]\[
\text{Total Change} = \text{Final Temperature} - \text{Initial Temperature}
\][/tex]
- Substituting the values:
[tex]\[
\text{Total Change} = 5.9 \,^\circ F - (-8.4 \,^\circ F)
\][/tex]
- This simplifies to:
[tex]\[
\text{Total Change} = 5.9 \,^\circ F + 8.4 \,^\circ F = 14.3 \,^\circ F
\][/tex]
3. Determine the total number of hours between the two times:
- From 4:00 AM to 2:00 PM, the time difference is:
[tex]\[
2:00 PM - 4:00 AM
\][/tex]
- Counting the hours: 4:00 AM to 8:00 AM is 4 hours, 8:00 AM to 11:00 AM is 3 hours, and 11:00 AM to 2:00 PM is 3 hours.
- Summing these intervals:
[tex]\[
4 + 3 + 3 = 10 \text{ hours}
\][/tex]
4. Calculate the average change per hour:
- The formula for the average change per hour is:
[tex]\[
\text{Average Change per Hour} = \frac{\text{Total Change in Temperature}}{\text{Total Hours}}
\][/tex]
- Substituting the values:
[tex]\[
\text{Average Change per Hour} = \frac{14.3 \,^\circ F}{10 \text{ hours}}
\][/tex]
- This simplifies to:
[tex]\[
\text{Average Change per Hour} = 1.43 \,^\circ F \text{ per hour}
\][/tex]
So, the average change per hour in the temperature between 4:00 AM and 2:00 PM was [tex]\(1.43^\circ F \text{ per hour}\)[/tex].
