To determine the rate of change in height above the canyon floor over time, we can use the values provided in the table:
- At time 0 minutes, the height is 360 feet.
- At time 3 minutes, the height is 280 feet.
- At time 10 minutes, the height is 160 feet.
- At time 14 minutes, the height is 80 feet.
We can calculate the change in height and the change in time to find the slope (rate of change):
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From 360 feet at time 0 to 280 feet at time 3: \[ \text{Change in height} = 280 - 360 = -80 \text{ feet} \] \[ \text{Change in time} = 3 - 0 = 3 \text{ minutes} \] \[ \text{Rate of change} = \frac{-80 \text{ feet}}{3 \text{ minutes}} \approx -26.67 \text{ feet per minute} \]
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From 280 feet at time 3 to 160 feet at time 10: \[ \text{Change in height} = 160 - 280 = -120 \text{ feet} \] \[ \text{Change in time} = 10 - 3 = 7 \text{ minutes} \] \[ \text{Rate of change} = \frac{-120 \text{ feet}}{7 \text{ minutes}} \approx -17.14 \text{ feet per minute} \]
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From 160 feet at time 10 to 80 feet at time 14: \[ \text{Change in height} = 80 - 160 = -80 \text{ feet} \] \[ \text{Change in time} = 14 - 10 = 4 \text{ minutes} \] \[ \text{Rate of change} = \frac{-80 \text{ feet}}{4 \text{ minutes}} = -20 \text{ feet per minute} \]
The average rate of change in height above the canyon floor from the table is approximately -20 feet per minute, which indicates that the elevation is decreasing as time increases.
Now, let's analyze the options given in the question:
- The statement that correctly describes this scenario is: The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.
This option accurately conveys that the height is decreasing (thus the negative sign) and reflects the action of descending to the canyon floor.