To determine the rate of change based on the given table, we can analyze the height changes over time.
From the table, we see the following height changes:
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From 360 ft to 280 ft in 3 minutes: \[ \frac{360 - 280}{3} = \frac{80}{3} \approx 26.67 \text{ ft/min (down)} \]
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From 280 ft to 160 ft in 7 minutes (10 min - 3 min): \[ \frac{280 - 160}{7} = \frac{120}{7} \approx 17.14 \text{ ft/min (down)} \]
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From 160 ft to 80 ft in 4 minutes (14 min - 10 min): \[ \frac{160 - 80}{4} = \frac{80}{4} = 20 \text{ ft/min (down)} \]
Calculating the rate of change between the first and last heights (360 ft to 80 ft over 14 minutes):
Total change in height: \[ 360 - 80 = 280 \text{ ft} \] Total time: \[ 14 \text{ min} \] Rate of change: \[ \frac{360 - 80}{14} = \frac{280}{14} = 20 \text{ ft/min (down)} \]
Based on this analysis, the rate of change of height for the hiker is negative, indicating a descent.
Therefore, the correct interpretation 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 correct answer is: The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.