Use the table to answer the question.Height Above Canyon Floor Time (minutes)360 0280 3160 1080 14Which statement best interprets the rate of change of the linear model shown in the table? (1 point)ResponsesThe 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 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 up from 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 negative 20 feet per minute.

Question

Use the table to answer the question.Height Above Canyon Floor Time (minutes)360 0280 3160 1080 14Which statement best interprets the rate of change of the linear model shown in the table? (1 point)ResponsesThe 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 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 up from 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 negative 20 feet per minute.

GPT-4o mini · Answer

To determine the rate of change from the table provided, we can analyze the given data points:

At time 0 minutes, the height is 360 feet.
At time 2 minutes, the height is 280 feet.
At time 3 minutes, the height is 160 feet.
At time 10 minutes, the height is 80 feet.
At time 14 minutes, the height is 0 feet (canyon floor).

We can notice that the height decreases as time increases. Let's find the change in height over the time interval to find the average rate of change:

From 0 to 2 minutes: Change in height = 280 - 360 = -80 feet Time = 2 - 0 = 2 minutes Rate of change = -80 feet / 2 minutes = -40 feet per minute
From 2 to 3 minutes: Change in height = 160 - 280 = -120 feet Time = 3 - 2 = 1 minute Rate of change = -120 feet / 1 minute = -120 feet per minute
From 3 to 10 minutes: Change in height = 80 - 160 = -80 feet Time = 10 - 3 = 7 minutes Rate of change = -80 feet / 7 minutes ≈ -11.43 feet per minute
From 10 to 14 minutes: Change in height = 0 - 80 = -80 feet Time = 14 - 10 = 4 minutes Rate of change = -80 feet / 4 minutes = -20 feet per minute

Considering the overall downward trend and the constant rate of -20 feet per minute between 10 and 14 minutes, the correct interpretation of the average rate of change for the linear model shown in the table 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 best response that aligns with this interpretation is:

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