To determine the rate of change in height above the canyon floor over time from the provided data, we need to analyze the changes in height relative to the time intervals:
-
From 0 to 3 minutes:
- Height changes from 360 to 280.
- Change in height = 360 - 280 = 80 feet decrease.
- Time interval = 3 minutes.
- Rate of change = \( \frac{-80 \text{ feet}}{3 \text{ minutes}} \approx -26.67 \text{ feet per minute} \).
-
From 3 to 10 minutes:
- Height changes from 280 to 160.
- Change in height = 280 - 160 = 120 feet decrease.
- Time interval = 10 - 3 = 7 minutes.
- Rate of change = \( \frac{-120 \text{ feet}}{7 \text{ minutes}} \approx -17.14 \text{ feet per minute} \).
-
From 10 to 14 minutes:
- Height changes from 160 to 80.
- Change in height = 160 - 80 = 80 feet decrease.
- Time interval = 14 - 10 = 4 minutes.
- Rate of change = \( \frac{-80 \text{ feet}}{4 \text{ minutes}} = -20 \text{ feet per minute} \).
The rate of change of -20 feet per minute is consistent over the last interval (10 to 14 minutes).
Thus, the best interpretation of the rate of change relates to a hiker who is moving down toward the canyon floor. Since the elevation is decreasing, the correct statement is:
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.