To determine the rate of change of the linear model from the table, we can look at the change in height over time.
From the table, we see the following data points:
- At 0 minutes: Height is 360 feet
- At 3 minutes: Height is 280 feet
- At 10 minutes: Height is 160 feet
- At 14 minutes: Height is 80 feet
Now, we can calculate the rate of change in height over time:
-
From 0 to 3 minutes: Change in height = 280 - 360 = -80 feet Time = 3 - 0 = 3 minutes Rate = -80 feet / 3 minutes ≈ -26.67 feet per minute
-
From 3 to 10 minutes: Change in height = 160 - 280 = -120 feet Time = 10 - 3 = 7 minutes Rate = -120 feet / 7 minutes ≈ -17.14 feet per minute
-
From 10 to 14 minutes: Change in height = 80 - 160 = -80 feet Time = 14 - 10 = 4 minutes Rate = -80 feet / 4 minutes = -20 feet per minute
The consistent rate of height change from 10 to 14 minutes is -20 feet per minute, indicating that the hiker is descending.
Based on the options provided and the calculated negative rate, the best interpretation of the rate of change of the linear model is:
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.