High School

In January 2008, the temperature in parts of Minnesota fell from [tex]$41^{\circ} F$[/tex] to [tex]$-13^{\circ} F$[/tex] over a 24-hour period. What was the average temperature change per hour?

A. [tex]\left(1 \frac{1}{6}\right)^{\circ} F[/tex]
B. [tex]-2.25^{\circ} F[/tex]
C. [tex]-\left(1 \frac{1}{6}\right)^{\circ} F[/tex]
D. [tex]2.25^{\circ} F[/tex]

Answer :

To find the average temperature change per hour, we need to follow these steps:

1. Calculate the Total Temperature Change:
- The temperature started at [tex]\(41^\circ F\)[/tex] and fell to [tex]\(-13^\circ F\)[/tex].
- The total change in temperature is calculated by subtracting the final temperature from the starting temperature:
[tex]\[
\text{Total temperature change} = -13 - 41 = -54^\circ F
\][/tex]
This means the temperature dropped [tex]\(54^\circ F\)[/tex] over the 24-hour period.

2. Calculate the Average Temperature Change per Hour:
- We need to find out how much the temperature changed per hour over the 24-hour period.
- To do this, divide the total temperature change by the number of hours:
[tex]\[
\text{Average temperature change per hour} = \frac{-54}{24} = -2.25^\circ F
\][/tex]

This calculation tells us that, on average, the temperature decreased by [tex]\(-2.25^\circ F\)[/tex] each hour.

Therefore, the correct answer is [tex]\(-2.25^\circ F\)[/tex].