To describe the rate of change in the relationship between the time (in hours) and the total amount of rainfall (in inches), we need to analyze the provided data more closely.
From the observations:
- At 1 hour, there are 1 inch of rainfall.
- At 2 hours, we have a value missing.
- At 3 hours, there are 2 inches of rainfall.
- At 4 hours, there are 3 inches of rainfall.
- At 5 hours, there are 5 inches of rainfall.
To find the rate of change, we can observe how the total rainfall increases with each passing hour. Based on the rainfall data provided:
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From 0 hours (before the first observation) to 1 hour:
- Rainfall increases from 0 to 1 inch.
- Change = 1 inch/1 hour = 1 inch per hour.
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From 1 hour to 2 hours:
- Since we do not have the value for 2 hours, we skip this for now.
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From 2 hours to 3 hours:
- Let's assume it was incremental; we can guess missing value or find a better pattern in between. Assuming constant growth is common in such scenarios.
- We have 2 inches at 3 hours and 1 inch at 1 hour.
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From 3 hours to 4 hours:
- Rainfall increases from 2 to 3 inches.
- Change = 3 inches - 2 inches = 1 inch over 1 hour = 1 inch per hour.
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From 4 hours to 5 hours:
- Rainfall increases from 3 to 5 inches.
- Change = 5 inches - 3 inches = 2 inches over 1 hour = 2 inches per hour.
Now if we average these points we notice: From the interval hours that we do know, the average rate of increase appears consistent as 1 inch per hour.
Thus, we conclude that the rate of change for this relationship is approximately:
The amount of rainfall increases by about 1 inch per hour.
However, it shows sudden growth of 2 inches at max, suggesting variations due to different conditions or possibly heavy bursts of rain at specific hours. Hence an average or linear estimate suffices here to describe the relationship established.
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