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Use the table to answer the question.

Applying the provided information to analyze the rate of decline in height above the canyon floor over time.
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 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 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 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.
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1 answer

To determine the rate of change in height above the canyon floor over time, we can analyze the data provided in the table:

  • From 0 to 3 minutes: height changes from 360 to 280, which is a decrease of 80 feet over 3 minutes.
  • From 3 to 10 minutes: height changes from 280 to 160, which is a decrease of 120 feet over 7 minutes.
  • From 10 to 14 minutes: height changes from 160 to 80, which is a decrease of 80 feet over 4 minutes.

To find the overall rate of change in height, we can look at the total change in height from the starting height (360 feet) to the final height (80 feet) over the total time (14 minutes).

  1. Calculate the total change in height:

    • Initial height: 360 feet
    • Final height: 80 feet
    • Change in height: 360 - 80 = 280 feet

  2. Calculate the total time:

    • 14 minutes (from 0 to 14 minutes)

  3. Now, calculate the rate of change:

    • Rate of change = total change in height / total time
    • Rate of change = 280 feet / 14 minutes = 20 feet per minute

Since the hiker is moving down towards the canyon floor, the rate of change can be expressed as negative:

  • Rate of change = -20 feet per minute (indicating a decrease in height).

Therefore, based on this analysis, the correct interpretation of the rate of change is:

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