Question

The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

Write a function rule that models this situation:

y=

Answer 1

Number of meals dispensed: 1 3 6 7
Amount of pet food remaining: 21 15 6 3

Answer 2

To create a function rule that models the amount of pet food remaining in an automatic feeder as a function of the number of meals dispensed, we need two key pieces of information: the initial amount of food in the feeder and the amount dispensed per meal.

Let's say:

- The initial amount of pet food in cups is \( C \).
- The amount of pet food dispensed per meal is \( D \).

If \( x \) represents the number of meals dispensed, then the amount of pet food remaining, \( y \), can be modeled by the following function:

\[
y = C - D \cdot x
\]

### Explanation:
- \( C \): the initial amount of food in the feeder (in cups).
- \( D \): the amount of food dispensed per meal (in cups).
- \( x \): the number of meals dispensed.
- \( y \): the amount of food remaining after \( x \) meals.

If you provide the specific values for \( C \) and \( D \), I can give you the exact function rule with those values plugged in!

Answer 3

To model the relationship between the number of meals dispensed and the amount of pet food remaining in the feeder, we will first analyze the data you provided:

- Number of meals dispensed (x): 1, 3, 6, 7
- Amount of pet food remaining (y): 21, 15, 6, 3

We can observe the changes:

1. Between 1 meal and 3 meals:
- 21 cups - 15 cups = 6 cups (for 2 meals)
- So, each meal dispenses \( 6/2 = 3 \) cups.

2. Between 3 meals and 6 meals:
- 15 cups - 6 cups = 9 cups (for 3 meals)
- So, each meal dispenses \( 9/3 = 3 \) cups (consistent).

3. Between 6 meals and 7 meals:
- 6 cups - 3 cups = 3 cups (for 1 meal)
- Again, this indicates 3 cups per meal.

Since the amount dispensed per meal is consistent at 3 cups, we can conclude:

- Initial amount of pet food \( C = 21 \) cups (when no meals have been dispensed).
- Amount dispensed per meal \( D = 3 \) cups.

Using this information, we can write the function rule as follows:

\[
y = 21 - 3x
\]

### Summary:
The function rule that models the amount of pet food remaining in cups as a function of the number of meals dispensed is:

\[
y = 21 - 3x
\]

where \( x \) is the number of meals dispensed.