To model the situation with a function rule, we first need to analyze the data you've provided. The relationship between the number of meals dispersed (x) and the amount of pet food remaining (y) can be described using the following pairs from your table:
- For \( x = 1 \), \( y = 25 \)
- For \( x = 3 \), \( y = 17 \)
- For \( x = 5 \), \( y = 9 \)
- For \( x = 7 \), \( y = 1 \)
Next, we can determine how much pet food is dispensed per meal by calculating the difference in the amount of food remaining for each pair of meals:
- From 1 to 3 meals: \( 25 - 17 = 8 \) cups consumed for 2 meals, so \( \frac{8}{2} = 4 \) cups per meal.
- From 3 to 5 meals: \( 17 - 9 = 8 \) cups consumed for 2 meals, so \( \frac{8}{2} = 4 \) cups per meal.
- From 5 to 7 meals: \( 9 - 1 = 8 \) cups consumed for 2 meals, so \( \frac{8}{2} = 4 \) cups per meal.
Thus, the feeder dispenses 4 cups of food per meal consistently.
Given that the initial amount of pet food is 25 cups, we can create a linear expression for the amount of food remaining \( y \) as a function of the number of meals \( x \).
We can express this as:
\[ y = 25 - 4x \]
where:
- \( y \) is the amount of pet food remaining,
- \( x \) is the number of meals dispersed.
So the function rule that models the situation is:
\[ y = 25 - 4x \]