To find the rate of change from the provided data, we can look at the change in height over the change in time. Let's analyze the first two readings in the table:
- From 360 feet to 280 feet (a change of 80 feet) occurs over 3 minutes (from 0 to 3 minutes).
- The calculation for the average rate of change during this interval is:
\[ \text{Rate of change} = \frac{\text{Change in height}}{\text{Change in time}} = \frac{360 - 280}{3 - 0} = \frac{80}{3} \approx 26.67 \text{ feet per minute} \]
However, since the height is decreasing, the rate of change would be negative.
Continuing this calculation for the next intervals, we see a pattern:
- From 280 to 160 feet (a change of 120 feet) over 7 minutes (from 3 to 10 minutes).
- The rate is:
\[ \text{Rate of change} = \frac{280 - 160}{10 - 3} = \frac{120}{7} \approx 17.14 \text{ feet per minute (negative)} \]
- From 160 to 80 feet (a change of 80 feet) over 4 minutes (from 10 to 14 minutes).
- The rate is:
\[ \text{Rate of change} = \frac{160 - 80}{14 - 10} = \frac{80}{4} = 20 \text{ feet per minute (negative)} \]
When we consolidate the observations, we can generalize that the final calculated average rate of change for the intervals shows that the elevation is decreasing overall, and thus the rate of change can be approximated as negative 20 feet per minute to capture the general trend meaning it can be lumped into the broader understanding of moving downwards.
Now, looking at the options given, the correct response indicating that the elevation is changing downwards is:
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.
This statement accurately reflects that despite the exact intervals' average rates differing slightly, the overall trend is downwards, confirming the negative rate of change.
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