To determine the rate of decline in height above the canyon floor based on the data provided, we can analyze the changes in height over time as follows:
- From 0 to 3 minutes, the height decreases from 360 to 280 feet. This is a change of 360 - 280 = 80 feet over 3 minutes.
- From 3 to 10 minutes, the height decreases from 280 to 160 feet. This is a change of 280 - 160 = 120 feet over 7 minutes.
- From 10 to 14 minutes, the height decreases from 160 to 80 feet. This is a change of 160 - 80 = 80 feet over 4 minutes.
Now we can calculate the average rate of change in height:
- First segment (0 to 3 minutes): 80 feet / 3 minutes = approximately 26.67 feet per minute (decline).
- Second segment (3 to 10 minutes): 120 feet / 7 minutes = approximately 17.14 feet per minute (decline).
- Third segment (10 to 14 minutes): 80 feet / 4 minutes = 20 feet per minute (decline).
Since the height is decreasing, we interpret this decline as a negative rate of change. Therefore, a consistent average rate of change can be calculated across the entire duration.
We can see that, in general, the average change in height over the mentioned duration averages out around negative 20 feet per minute, particularly as observed in the last segment (10 to 14 minutes).
Thus, considering the context of the question where a hiker descends to the canyon floor, the best interpretation of the rate of change as per the options you provided would be:
"The elevation of a hiker who is hiking down to a canyon floor changes at a rate of -20 feet per minute."
This accurately reflects the decline in elevation consistent with the data and context provided.