Question
Question
Use the table to answer the question.
Height Above 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 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 negative 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.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
Use the table to answer the question.
Height Above 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 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 negative 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.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
Answers
Answered by
GPT-4o mini
To determine the rate of change of the height above the canyon floor over time, we can analyze the height data provided in the table. The height above the canyon floor decreases as time increases.
From the data:
- 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 rate of change, we can look at the change in height with respect to the change in time between two points:
1. From 0 to 3 minutes:
\[
\text{Change in height} = 280 - 360 = -80 \text{ feet}
\]
\[
\text{Change in time} = 3 - 0 = 3 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-80}{3} \approx -26.67 \text{ feet per minute}
\]
2. From 3 to 10 minutes:
\[
\text{Change in height} = 160 - 280 = -120 \text{ feet}
\]
\[
\text{Change in time} = 10 - 3 = 7 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-120}{7} \approx -17.14 \text{ feet per minute}
\]
3. From 10 to 14 minutes:
\[
\text{Change in height} = 80 - 160 = -80 \text{ feet}
\]
\[
\text{Change in time} = 14 - 10 = 4 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-80}{4} = -20 \text{ feet per minute}
\]
From the overall analysis, it appears that the average rate of change in height is approximately -20 feet per minute, indicating a decrease in elevation as time goes on.
Considering the appropriate interpretation of this rate:
- Since the height is decreasing, the statement that correctly reflects this change is: **The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.**
Thus, the correct response is:
**The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.**
From the data:
- 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 rate of change, we can look at the change in height with respect to the change in time between two points:
1. From 0 to 3 minutes:
\[
\text{Change in height} = 280 - 360 = -80 \text{ feet}
\]
\[
\text{Change in time} = 3 - 0 = 3 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-80}{3} \approx -26.67 \text{ feet per minute}
\]
2. From 3 to 10 minutes:
\[
\text{Change in height} = 160 - 280 = -120 \text{ feet}
\]
\[
\text{Change in time} = 10 - 3 = 7 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-120}{7} \approx -17.14 \text{ feet per minute}
\]
3. From 10 to 14 minutes:
\[
\text{Change in height} = 80 - 160 = -80 \text{ feet}
\]
\[
\text{Change in time} = 14 - 10 = 4 \text{ minutes}
\]
\[
\text{Rate of change} = \frac{-80}{4} = -20 \text{ feet per minute}
\]
From the overall analysis, it appears that the average rate of change in height is approximately -20 feet per minute, indicating a decrease in elevation as time goes on.
Considering the appropriate interpretation of this rate:
- Since the height is decreasing, the statement that correctly reflects this change is: **The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.**
Thus, the correct response is:
**The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.**