To determine the rate of change from the provided table, we can calculate the change in height over the change in time.
-
Identify the changes:
- From 360 feet to 280 feet (360 - 280 = 80 feet) over 3 minutes (3 - 0 = 3 minutes).
- From 280 feet to 160 feet (280 - 160 = 120 feet) over 7 minutes (10 - 3 = 7 minutes).
- From 160 feet to 80 feet (160 - 80 = 80 feet) over 4 minutes (14 - 10 = 4 minutes).
-
Calculate the average rate of change:
- For the first interval (360 to 280): \( \frac{-80 \text{ feet}}{3 \text{ minutes}} \approx -26.67 \text{ feet per minute} \)
- For the second interval (280 to 160): \( \frac{-120 \text{ feet}}{7 \text{ minutes}} \approx -17.14 \text{ feet per minute} \)
- For the third interval (160 to 80): \( \frac{-80 \text{ feet}}{4 \text{ minutes}} = -20 \text{ feet per minute} \)
The consistent rate of change toward the canyon is approximately -20 feet per minute for the last interval.
- Interpretation: Given the consistent and negative nature of the height change, the correct interpretation of the rate of change is:
"The elevation of a hiker who is hiking down to a canyon floor changes at a rate of -20 feet per minute."
Thus, the best response from the provided options is:
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.