Question

The formula f(x)=3x+72 represents the temperature of water put to boil, in degrees Fahrenheit, after leaving it on the stove for x minutes. Calculate the average temperature change between two and five minutes.

Answer 1

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 \( f(x) = 3x + 72 \).

1. **Calculate the temperature at 2 minutes**:
\[
f(2) = 3(2) + 72 = 6 + 72 = 78 \text{ degrees Fahrenheit}
\]

2. **Calculate the temperature at 5 minutes**:
\[
f(5) = 3(5) + 72 = 15 + 72 = 87 \text{ degrees Fahrenheit}
\]

3. **Calculate the temperature change**:
The temperature change from 2 minutes to 5 minutes is:
\[
\Delta T = f(5) - f(2) = 87 - 78 = 9 \text{ degrees Fahrenheit}
\]

4. **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**.