To determine the average rate of change of the height of the water in the rain barrel during the given time period, we need to follow these steps:
1. Determine the total time elapsed:
- The rain started at 10:00 am and continued until 11:40 am.
- First, let's calculate the difference in time.
2. Convert the time into minutes:
- From 10:00 am to 11:00 am is 60 minutes.
- From 11:00 am to 11:40 am is 40 minutes.
- Therefore, the total time elapsed is [tex]\( 60 \text{ minutes} + 40 \text{ minutes} = 100 \text{ minutes} \)[/tex].
3. Determine the total change in height of the water:
- The water level increased by 4 inches during this period.
4. Calculate the average rate of change:
- The average rate of change is given by the formula:
[tex]\[
\text{Average Rate of Change} = \frac{\text{Total Change in Height}}{\text{Total Time Elapsed}}
\][/tex]
- Plugging in the known values:
[tex]\[
\text{Average Rate of Change} = \frac{4 \text{ inches}}{100 \text{ minutes}}
\][/tex]
5. Simplify the fraction:
- The average rate of change is:
[tex]\[
\frac{4}{100} = 0.04 \text{ inches/minute}
\][/tex]
Therefore, the average rate of change of the height of the water in the rain barrel during the specified time period is [tex]\( 0.04 \)[/tex] inches per minute.
