To model the scenario of Andre and Kara collecting food for the food pantry in an arithmetic sequence, let's first create a table and then construct a graph.
Table
Let \( n \) represent the number of people asked for donations, and since they receive an average of 13 items for each person, the number of items collected can be modeled with the formula:
\[ \text{Items} = 13n \]
Here's the table showing values for various numbers of people asked:
| Number of People (n) | Items Collected (y = 13n) | |----------------------|---------------------------| | 0 | 0 | | 1 | 13 | | 2 | 26 | | 3 | 39 | | 4 | 52 | | 5 | 65 | | 6 | 78 | | 7 | 91 | | 8 | 104 | | 9 | 117 | | 10 | 130 |
Graph
To create a graph, plot the values of \( n \) on the x-axis and the corresponding \( y \) values (items collected) on the y-axis.
- X-axis: Number of People Asked (n)
- Y-axis: Total Items Collected (y)
Y-axis Label
The most appropriate label for the y-axis in this scenario would be "Total Items Collected" since it clearly indicates what quantity is being measured as a function of the number of people asked.
In summary, the table provides a clear arithmetic sequence with a common difference of 13, reflecting the consistent increase in total items collected as more people are asked for donations.