Question
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)
0
3
360
280
160
10
80
14
Which statement best interprets the rate of change of the linear model shown in the table?
(1 point)
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
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
Applying the provided information to analyze the rate of decline in height above the canyon floor over time.
Height Above Canyon Floor
Time (minutes)
0
3
360
280
160
10
80
14
Which statement best interprets the rate of change of the linear model shown in the table?
(1 point)
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
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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the rate of decline in height above the canyon floor over time using a linear model, we first need to establish the relationship between the height and time based on the given data.
From the provided data, we need to observe how the height changes as the time progresses:
1. At time 0 minutes, the height is 360 feet.
2. At time 3 minutes, the height is 280 feet.
3. At time 10 minutes, the height is 160 feet.
4. At time 14 minutes, the height is 80 feet.
Now, we can calculate the change in height over the change in time to determine the rate of decline:
- From 360 to 280 (0 to 3 minutes):
Change in height = 360 - 280 = 80 feet
Change in time = 3 - 0 = 3 minutes
Rate = 80 feet / 3 minutes ≈ 26.67 feet per minute
- From 280 to 160 (3 to 10 minutes):
Change in height = 280 - 160 = 120 feet
Change in time = 10 - 3 = 7 minutes
Rate = 120 feet / 7 minutes ≈ 17.14 feet per minute
- From 160 to 80 (10 to 14 minutes):
Change in height = 160 - 80 = 80 feet
Change in time = 14 - 10 = 4 minutes
Rate = 80 feet / 4 minutes = 20 feet per minute
The last calculation shows that the elevation declines at a rate of 20 feet per minute at one segment.
Given this analysis, the best option that interprets the rate of change from the table is:
**The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.**
Hence, this is the correct answer.
From the provided data, we need to observe how the height changes as the time progresses:
1. At time 0 minutes, the height is 360 feet.
2. At time 3 minutes, the height is 280 feet.
3. At time 10 minutes, the height is 160 feet.
4. At time 14 minutes, the height is 80 feet.
Now, we can calculate the change in height over the change in time to determine the rate of decline:
- From 360 to 280 (0 to 3 minutes):
Change in height = 360 - 280 = 80 feet
Change in time = 3 - 0 = 3 minutes
Rate = 80 feet / 3 minutes ≈ 26.67 feet per minute
- From 280 to 160 (3 to 10 minutes):
Change in height = 280 - 160 = 120 feet
Change in time = 10 - 3 = 7 minutes
Rate = 120 feet / 7 minutes ≈ 17.14 feet per minute
- From 160 to 80 (10 to 14 minutes):
Change in height = 160 - 80 = 80 feet
Change in time = 14 - 10 = 4 minutes
Rate = 80 feet / 4 minutes = 20 feet per minute
The last calculation shows that the elevation declines at a rate of 20 feet per minute at one segment.
Given this analysis, the best option that interprets the rate of change from the table is:
**The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.**
Hence, this is the correct answer.
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