To determine the rate of change based on the table provided, we can observe the height above the canyon floor and the corresponding time.
From the data:
- At 0 minutes, the height is 360 feet.
- At 3 minutes, the height is 280 feet.
- At 10 minutes, the height is 160 feet.
- At 14 minutes, the height is 80 feet.
To find the rate of change, we can calculate the change in height over the change in time:
-
From 360 feet to 280 feet (0 to 3 minutes):
- Change in height: 280 - 360 = -80 feet
- Time taken: 3 - 0 = 3 minutes
- Rate of change: -80 feet / 3 minutes = -26.67 feet per minute
-
From 280 feet to 160 feet (3 to 10 minutes):
- Change in height: 160 - 280 = -120 feet
- Time taken: 10 - 3 = 7 minutes
- Rate of change: -120 feet / 7 minutes = -17.14 feet per minute
-
From 160 feet to 80 feet (10 to 14 minutes):
- Change in height: 80 - 160 = -80 feet
- Time taken: 14 - 10 = 4 minutes
- Rate of change: -80 feet / 4 minutes = -20 feet per minute
This shows a consistent rate of descent of -20 feet per minute from 10 to 14 minutes.
Since the overall observation shows a decline in height, we can conclude:
The statement that best interprets the rate of change is:
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.