In this scenario, since Andre and Kara receive an average of 13 items for every person they ask to donate, it is most appropriate to label the y-axis "number of items donated." This accurately represents the output of the arithmetic sequence as it relates to the individuals they approach.
Here is how you could set up a table and the corresponding arithmetic sequence for the number of items donated based on the number of people asked to donate:
Table:
| Number of People Asked to Donate (x) | Number of Items Donated (y) | |---------------------------------------|------------------------------| | 0 | 0 | | 1 | 13 | | 2 | 26 | | 3 | 39 | | 4 | 52 | | 5 | 65 |
Arithmetic Sequence:
The arithmetic sequence can be expressed as:
- First term (a) = 0 (when no one is asked)
- Common difference (d) = 13 (the number of items received for each additional person asked)
The formula for the \(n\)-th term of an arithmetic sequence is: \[ a_n = a + (n - 1)d \] Substituting the values: \[ a_n = 0 + (n - 1) \cdot 13 \] This simplifies to: \[ a_n = 13(n - 1) \]
Graph:
When graphing this sequence, the x-axis represents the number of people asked to donate, and the y-axis represents the number of items donated.
In conclusion, the most appropriate label for the y-axis is "number of items donated."