To find the rate of change, we need to determine how much the distance changes for a given change in time.
Let's look at the data provided:
- At 3 minutes, the distance is 36 miles.
- At 5 minutes, the distance is 60 miles.
- At 7 minutes, the distance is 84 miles.
- At 9 minutes, the distance is 108 miles.
- At 11 minutes, the distance is 132 miles.
We can calculate the change in distance and the change in time between two points:
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From 3 to 5 minutes:
- Distance increases from 36 to 60 miles.
- Change in distance = \(60 - 36 = 24\) miles.
- Change in time = \(5 - 3 = 2\) minutes.
- Rate of change = \( \frac{24 \text{ miles}}{2 \text{ minutes}} = 12 \text{ miles per minute}\).
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From 5 to 7 minutes:
- Distance increases from 60 to 84 miles.
- Change in distance = \(84 - 60 = 24\) miles.
- Change in time = \(7 - 5 = 2\) minutes.
- Rate of change = \( \frac{24 \text{ miles}}{2 \text{ minutes}} = 12 \text{ miles per minute}\).
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From 7 to 9 minutes:
- Distance increases from 84 to 108 miles.
- Change in distance = \(108 - 84 = 24\) miles.
- Change in time = \(9 - 7 = 2\) minutes.
- Rate of change = \( \frac{24 \text{ miles}}{2 \text{ minutes}} = 12 \text{ miles per minute}\).
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From 9 to 11 minutes:
- Distance increases from 108 to 132 miles.
- Change in distance = \(132 - 108 = 24\) miles.
- Change in time = \(11 - 9 = 2\) minutes.
- Rate of change = \( \frac{24 \text{ miles}}{2 \text{ minutes}} = 12 \text{ miles per minute}\).
From all these calculations, we can see that the rate of change remains constant at \(12\) miles per minute.
Looking at the answer options provided, the correct response is: 12; 12 miles per minute.
1 answer