Bot GPT 4-o mini To model the situation with a function rule, we need to analyze the relationship between the number of meals dispensed (x) and the amount of pet food remaining (y).
From the table, we have the following data points:
- For 2 meals dispensed (x = 2), the amount remaining (y) is 33 cups.
- For 5 meals dispensed (x = 5), y is 27 cups.
- For 11 meals dispensed (x = 11), y is 15 cups.
To find a function that relates x and y, we can observe how the amount of pet food decreases with each meal dispensed.
We can calculate the difference in y as x increases:
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From 2 meals to 5 meals (a difference of 3 meals), the change in y is: \(27 - 33 = -6\) cups. This means that dispensing 3 meals results in a decrease of 6 cups, which gives us: \(-6 / 3 = -2\) cups per meal.
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From 5 meals to 11 meals (a difference of 6 meals), the change in y is: \(15 - 27 = -12\) cups. Thus, dispensing 6 meals results in a decrease of 12 cups, which gives us: \(-12 / 6 = -2\) cups per meal.
Since the amount of pet food decreases by 2 cups for each meal dispensed, we can express the relationship with the point-slope form of a linear function.
Now, starting from 33 cups when 2 meals have been dispensed, we can write:
\[ y = 33 - 2(x - 2) \]
Distributing this gives:
\[ y = 33 - 2x + 4 \]
Which simplifies to:
\[ y = 37 - 2x \]
So, the function rule that models this situation is:
\[ y = 37 - 2x \]
Where:
- \(y\) is the amount of pet food remaining (in cups),
- \(x\) is the number of meals dispensed.
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