To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio of the number of apples to the number of trees remains constant for all entries.
Let's calculate the ratio of apples to trees for each row in the table:
- For 2 trees: 26 apples → Ratio = \( \frac{26}{2} = 13 \)
- For 3 trees: 39 apples → Ratio = \( \frac{39}{3} = 13 \)
- For 6 trees: 78 apples → Ratio = \( \frac{78}{6} = 13 \)
- For 10 trees: 130 apples → Ratio = \( \frac{130}{10} = 13 \)
- For 12 trees: 156 apples → Ratio = \( \frac{156}{12} = 13 \)
Since the ratio of apples to trees is the same (13) for all entries, we conclude that the quantities in the data table are in a proportional relationship.
The correct response is:
Yes, the data table has a proportional relationship.