Use the table to answer the question.

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 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 −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.

Answer 1

To determine the rate of change from the table, we can look at the change in height over the change in time:

• From 360 feet to 280 feet in 3 minutes: Change in height = 280 - 360 = -80 feet Change in time = 3 - 0 = 3 minutes Rate of change = -80 feet / 3 minutes = -26.67 feet/minute (approximately -27 feet/minute)

• From 280 feet to 160 feet in 7 minutes (10 - 3): Change in height = 160 - 280 = -120 feet Change in time = 10 - 3 = 7 minutes Rate of change = -120 feet / 7 minutes = -17.14 feet/minute (approximately -17 feet/minute)

• From 160 feet to 80 feet in 4 minutes (14 - 10): Change in height = 80 - 160 = -80 feet Change in time = 14 - 10 = 4 minutes Rate of change = -80 feet / 4 minutes = -20 feet/minute

By observing these calculations, we notice that the rate of change of -20 feet/minute is consistent between the heights of 160 feet and 80 feet over the time span of 4 minutes.

Given these observations, the best interpretation from the options provided is:

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