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Use the table to answer the question. Height Above Canyon Floor Time (minutes) 360 0 280 3 160 10 80 14 Which statement best interprets the rate of change of the linear model shown in the table? (1 point) Responses The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute. The elevation of a hiker who is hiking up from canyon floor changes at a rate of −20 feet per minute.

1 answer

To determine the rate of change based on the provided table, we can analyze the height above the canyon floor at different time intervals:

  • From 360 feet at 0 minutes to 280 feet at 3 minutes, the change in height is \( 360 - 280 = 80 \) feet over \( 3 \) minutes.
  • From 280 feet at 3 minutes to 160 feet at 10 minutes, the change in height is \( 280 - 160 = 120 \) feet over \( 7 \) minutes.
  • From 160 feet at 10 minutes to 80 feet at 14 minutes, the change in height is \( 160 - 80 = 80 \) feet over \( 4 \) minutes.

Now, calculating the average rate of change:

  1. First Interval: \[ \text{Rate} = \frac{-80 \text{ feet}}{3 \text{ minutes}} = -\frac{80}{3} \approx -26.67 \text{ feet per minute} \]

  2. Second Interval: \[ \text{Rate} = \frac{-120 \text{ feet}}{7 \text{ minutes}} = -\frac{120}{7} \approx -17.14 \text{ feet per minute} \]

  3. Third Interval: \[ \text{Rate} = \frac{-80 \text{ feet}}{4 \text{ minutes}} = -20 \text{ feet per minute} \]

The most relevant consistent rate of change is \(-20\) feet per minute during the last interval, which indicates a descent.

Thus, the best interpretation among the options given is:

The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.