Questions: The most freakish change in temperature ever recorded was from -4°F to 45°F between 7:30 am and 7:32 am on January 22, 1943 at Spearfish, South Dakota. [1] What was the average rate of change of the temperature for this time period? NOTE: Enter the exact answer.

The most freakish change in temperature ever recorded was from -4°F to 45°F between 7:30 am and 7:32 am on January 22, 1943 at Spearfish, South Dakota. [1] What was the average rate of change of the temperature for this time period? NOTE: Enter the exact answer.
Transcript text: The most freakish change in temperature ever recorded was from $-4^{\circ} \mathrm{F}$ to $45^{\circ} \mathrm{F}$ between 7:30 am and 7:32 am on January 22, 1943 at Spearfish, South Dakota. ${ }^{1}$ What was the average rate of change of the temperature for this time period? NOTE: Enter the exact answer.
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Solution

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Solution Steps

To find the average rate of change of the temperature, we need to calculate the difference in temperature and divide it by the difference in time. The temperature changed from \(-4^{\circ} \mathrm{F}\) to \(45^{\circ} \mathrm{F}\) over a period of 2 minutes (from 7:30 am to 7:32 am).

Step 1: Identify Initial and Final Temperatures

The initial temperature is \(-4^{\circ} \mathrm{F}\) and the final temperature is \(45^{\circ} \mathrm{F}\).

Step 2: Calculate the Change in Temperature

The change in temperature is given by: \[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 45 - (-4) = 45 + 4 = 49^{\circ} \mathrm{F} \]

Step 3: Determine the Time Period

The time period over which the temperature change occurred is 2 minutes.

Step 4: Calculate the Average Rate of Change

The average rate of change of the temperature is given by: \[ \text{Average Rate of Change} = \frac{\Delta T}{\Delta t} = \frac{49}{2} = 24.5 \, \text{degrees per minute} \]

Final Answer

\[ \boxed{\frac{49}{2} \, \text{degrees per minute}} \]

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