A worker is packing items in boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.
Number of Minutes Number of Items Packed
5 20
7 28
11 44
14 56
Which statement describes the rate of change of the number of items the worker packed in boxes with respect to the number of minutes the worker has been packing items in boxes?
The worker packed 8 items in boxes per minute
The worker packed 37 items in boxes per minute
The worker packed 4 items in boxes per minute
The worker packed 15 items in boxes per minute
The correct statement is: The worker packed 4 items in boxes per minute.
This rate of change can be calculated by determining the difference in the number of items packed for each increase in time and then dividing by the difference in time.
(28 - 20) / (7 - 5) = 8 / 2 = 4 items per minute
(44 - 28) / (11 - 7) = 16 / 4 = 4 items per minute
(56 - 44) / (14 - 11) = 12 / 3 = 4 items per minute
Therefore, the rate of change of the number of items packed in boxes with respect to the number of minutes is 4 items per minute.