To determine the rate of change for the relationship between time (in days) and the amount of oatmeal left (in cups), we need to analyze the given data points.
The provided data points are as follows:
- Day 0: 4 cups
- Day 8: 20 cups
- Day 15: 10 cups
First, we’ll find the total change in the amount of oatmeal and the total time over the specified periods:
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Between day 0 and day 8:
- Amount of oatmeal change = 20 cups - 4 cups = 16 cups
- Time change = 8 days - 0 days = 8 days
- Rate of change = \( \frac{16 \text{ cups}}{8 \text{ days}} = 2 \text{ cups per day} \)
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Between day 8 and day 15:
- Amount of oatmeal change = 10 cups - 20 cups = -10 cups
- Time change = 15 days - 8 days = 7 days
- Rate of change = \( \frac{-10 \text{ cups}}{7 \text{ days}} \approx -1.43 \text{ cups per day} \)
To summarize:
- From Day 0 to Day 8, the amount of oatmeal increased by 2 cups per day.
- From Day 8 to Day 15, the amount of oatmeal decreased by approximately 1.43 cups per day.
If we are to describe the overall rate of change for the trip as a whole, we’d take the difference from the beginning to the end:
- At Day 0: 4 cups
- At Day 15: 10 cups
Overall change in oatmeal = 10 cups - 4 cups = 6 cups over 15 days.
Overall rate of change = \( \frac{6 \text{ cups}}{15 \text{ days}} = 0.4 \text{ cups per day} \).
In conclusion, the average rate of change for the amount of oatmeal left is approximately 0.4 cups per day.
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