Use the table to answer the question

Question

Height above Canyon floor Time (minutes)
360 0
280 3
160 10
80 14

Which statements best interprets the rate of change of the linear model shown in the table

answers:

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 canyon floor changes at a rate of -20 feet per minute

Answer 1

To determine the rate of change based on the data provided in the table, we can look at the height above the canyon floor at different times.

From the table:

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

To calculate the average rate of change in height per minute, we can find the change in height over the change in time between two points.

Let's calculate the overall rate of change between the first and the last points (from 360 feet to 80 feet over 14 minutes):

1. Change in height: 360 - 80 = 280 feet
2. Change in time: 14 - 0 = 14 minutes

Now we can calculate the rate of change:

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

Since the elevation is decreasing (the hiker is descending), the correct interpretation of this rate of change is negative. Therefore:

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

Answer 2

you sure

Answer 3

Let's break down the problem again to ensure the proper interpretation of the rate of change based on the data provided.

Data Analysis:

• At 0 minutes: Height = 360 feet
• At 3 minutes: Height = 280 feet
• At 10 minutes: Height = 160 feet
• At 14 minutes: Height = 80 feet

We can clearly see that as time increases, the height decreases.

Calculating the Rate of Change:

1. Between 0 minutes and 3 minutes:

   • Change in height = 280 - 360 = -80 feet
   • Time = 3 - 0 = 3 minutes
   • Rate of change = -80 feet / 3 minutes ≈ -26.67 feet per minute

2. Between 3 minutes and 10 minutes:

   • Change in height = 160 - 280 = -120 feet
   • Time = 10 - 3 = 7 minutes
   • Rate of change = -120 feet / 7 minutes ≈ -17.14 feet per minute

3. Between 10 minutes and 14 minutes:

   • Change in height = 80 - 160 = -80 feet
   • Time = 14 - 10 = 4 minutes
   • Rate of change = -80 feet / 4 minutes = -20 feet per minute

4. Overall from 0 minutes to 14 minutes:

   • Change in height = 80 - 360 = -280 feet
   • Time = 14 - 0 = 14 minutes
   • Rate of change = -280 feet / 14 minutes = -20 feet per minute

Final Conclusion

The hiker's height above the canyon floor decreases at a rate of -20 feet per minute for the overall duration from start to end. Therefore, the correct statement is:

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

Thank you for prompting a review; the original conclusion stands as accurate based on the calculations.