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?

Answer 1

To evaluate the rate of change of the number of items packed in boxes with respect to time, we can analyze the data presented in the table that shows the relationship between the number of items packed and the time taken.

The rate of change, or the slope of the line representing this linear relationship, is calculated by taking the difference in the number of items packed at two different time points and dividing that by the difference in time.

Mathematically, if we have two points (t1, i1) and (t2, i2) from the table, the rate of change (R) can be expressed as:

\[ R = \frac{i2 - i1}{t2 - t1} \]

This rate of change tells us how many items are packed per unit of time (e.g., per minute).

• If the rate of change is positive, it means that the worker is packing more items as time progresses.
• If the rate of change is negative, it would imply that the worker is packing fewer items over time.
• A constant positive rate of change indicates a consistent packing pace.

In the context of your question, the statement that represents the rate of change of the number of items packed in boxes with respect to time would indicate how many items the worker packs per minute, reflecting the efficiency and productivity of the worker during the packing operation.