To find the rate of change of the number of items packed with respect to the number of minutes, we need to determine how many items are packed per minute in the given time intervals.
Let's analyze the data provided:
-
Between 4 and 6 minutes (0 minutes to 2 minutes):
- Items packed at 4 minutes: 20
- Items packed at 6 minutes: 20
- Change in items packed: 20 - 20 = 0
- Change in time: 6 - 4 = 2 minutes
- Rate of change: 0 items / 2 minutes = 0 items per minute
-
Between 6 and 12 minutes (2 minutes to 8 minutes):
- Items packed at 6 minutes: 20
- Items packed at 12 minutes: 44
- Change in items packed: 44 - 20 = 24
- Change in time: 12 - 6 = 6 minutes
- Rate of change: 24 items / 6 minutes = 4 items per minute
-
Between 12 and 14 minutes (8 minutes to 10 minutes):
- Items packed at 12 minutes: 44
- Items packed at 14 minutes: 50
- Change in items packed: 50 - 44 = 6
- Change in time: 14 - 12 = 2 minutes
- Rate of change: 6 items / 2 minutes = 3 items per minute
Now summarizing the rate of change for each interval:
- From 4 to 6 minutes: 0 items per minute
- From 6 to 12 minutes: 4 items per minute
- From 12 to 14 minutes: 3 items per minute
The rate of change is not constant, as it varies based on the intervals. The worker starts slow, then increases the rate significantly, and then the rate decreases slightly.
In conclusion, the linear relationship indicates that the rate of change of the number of items packed with respect to time is variable and can be described as follows:
- Initially, no items were packed between 4 and 6 minutes (0 items/minute).
- Then, there was a faster rate of packing from 6 to 12 minutes (4 items/minute).
- Finally, the rate decreased to 3 items/minute from 12 to 14 minutes.
The average rate of change overall varies, predominantly increasing after the initial two minutes of no packing.