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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 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. 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 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.

1 answer

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

  • At time 0 minutes, the height is 360 feet.
  • At time 3 minutes, the height is 280 feet.
  • At time 10 minutes, the height is 160 feet.
  • At time 14 minutes, the height is 80 feet.

Now, let's calculate the rate of change between the points given.

  1. From 0 to 3 minutes:

    • Change in height: 360 - 280 = 80 feet
    • Change in time: 3 - 0 = 3 minutes
    • Rate of change: 80 feet / 3 minutes ≈ 26.67 feet per minute (this is a decrease).

  2. From 3 to 10 minutes:

    • Change in height: 280 - 160 = 120 feet
    • Change in time: 10 - 3 = 7 minutes
    • Rate of change: 120 feet / 7 minutes ≈ 17.14 feet per minute (this is a decrease).

  3. From 10 to 14 minutes:

    • Change in height: 160 - 80 = 80 feet
    • Change in time: 14 - 10 = 4 minutes
    • Rate of change: 80 feet / 4 minutes = 20 feet per minute (this is a decrease).

To find an average rate of change over the overall time:

  • Overall change in height: 360 - 80 = 280 feet
  • Overall change in time: 14 - 0 = 14 minutes
  • Average rate of change: 280 feet / 14 minutes = 20 feet per minute.

Since the height is decreasing as the minutes increase, we can conclude that the elevation of the hiker who is hiking down to the canyon floor changes at a rate of -20 feet per minute.

Among the responses, the appropriate interpretation based on this analysis would be:

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