To find the average temperature change of the boiling water between 2 and 5 minutes, we will first calculate the temperature at both time points using the formula \( f(x) = 3x + 72 \).
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Calculate the temperature at 2 minutes: \[ f(2) = 3(2) + 72 = 6 + 72 = 78 \text{ degrees Fahrenheit} \]
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Calculate the temperature at 5 minutes: \[ f(5) = 3(5) + 72 = 15 + 72 = 87 \text{ degrees Fahrenheit} \]
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Calculate the temperature change: The temperature change from 2 minutes to 5 minutes is: \[ \Delta T = f(5) - f(2) = 87 - 78 = 9 \text{ degrees Fahrenheit} \]
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Calculate the average temperature change: The average temperature change over the interval from 2 to 5 minutes is given by the total temperature change divided by the time interval: \[ \text{Average Temperature Change} = \frac{\Delta T}{\Delta t} = \frac{9}{5 - 2} = \frac{9}{3} = 3 \text{ degrees Fahrenheit per minute} \]
Therefore, the average temperature change between 2 and 5 minutes is 3 degrees Fahrenheit per minute.
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