Question

Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?(1 point)
Responses

food pantry
food pantry

number of people asked to donate
number of people asked to donate

number of items donated
number of items donated

neighborhood population

Answer 1

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."**