A worker is packing items in a boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.

Question

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?
Number of Minutes:4, 6,12,14
Number of Items :20,26,44,50

Answer 1

To analyze the rate of change of the number of items packed by the worker with respect to the number of minutes, we can calculate the rate of change using the information provided. The rate of change can be determined by finding the change in the number of items packed divided by the change in the number of minutes for different intervals.

Let's calculate the rate of change between the given points:

1. From 4 minutes to 6 minutes:

   • Change in items = 26 - 20 = 6
   • Change in minutes = 6 - 4 = 2
   • Rate of change = Change in items / Change in minutes = 6 / 2 = 3 items/minute

2. From 6 minutes to 12 minutes:

   • Change in items = 44 - 26 = 18
   • Change in minutes = 12 - 6 = 6
   • Rate of change = 18 / 6 = 3 items/minute

3. From 12 minutes to 14 minutes:

   • Change in items = 50 - 44 = 6
   • Change in minutes = 14 - 12 = 2
   • Rate of change = 6 / 2 = 3 items/minute

Since the rate of change is consistent across all intervals, we can conclude that the worker is packing items at a constant rate of 3 items per minute.

Thus, the statement that describes the rate of change of the number of items the worker packed in boxes with respect to the number of minutes would be that the worker packs 3 items per minute consistently over the given time intervals.