To determine if the quantities in the data table are in a proportional relationship, we can calculate the ratio of the number of apples to the number of trees for each pair of values.
Let's analyze the ratios:
- For 2 trees: \( \frac{26 \text{ apples}}{2 \text{ trees}} = 13 \)
- For 3 trees: \( \frac{39 \text{ apples}}{3 \text{ trees}} = 13 \)
- For 6 trees: \( \frac{78 \text{ apples}}{6 \text{ trees}} = 13 \)
- For 10 trees: \( \frac{130 \text{ apples}}{10 \text{ trees}} = 13 \)
- For 12 trees: \( \frac{156 \text{ apples}}{12 \text{ trees}} = 13 \)
Since the ratio of apples to trees is consistent (13) for all pairs of values, we can conclude that the quantities in the data table are in a proportional relationship.
The answer is: Yes, the data table has a proportional relationship.