Question
Dana uses her smartwatch to track how many steps she takes each day. Today, she walks to school and then walks around the track with her friends.
There is a linear relationship between the number of laps around the track Dana completes and the total number of steps she has taken so far today.
Number of laps Total number of steps
2 3,000
4 4,000
6 5,000
8 6,000
Describe the rate of change for this relationship.
The total number of steps Dana has taken today
by
per lap around the track.
There is a linear relationship between the number of laps around the track Dana completes and the total number of steps she has taken so far today.
Number of laps Total number of steps
2 3,000
4 4,000
6 5,000
8 6,000
Describe the rate of change for this relationship.
The total number of steps Dana has taken today
by
per lap around the track.
Answers
GPT-4o mini
To analyze the relationship between the number of laps Dana completes and the total number of steps she has taken, we can first determine the change in total steps for each lap she completes.
From the data provided:
- From 2 laps (3,000 steps) to 4 laps (4,000 steps):
Change in steps = 4,000 - 3,000 = 1,000 steps
Change in laps = 4 - 2 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
- From 4 laps (4,000 steps) to 6 laps (5,000 steps):
Change in steps = 5,000 - 4,000 = 1,000 steps
Change in laps = 6 - 4 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
- From 6 laps (5,000 steps) to 8 laps (6,000 steps):
Change in steps = 6,000 - 5,000 = 1,000 steps
Change in laps = 8 - 6 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
From this analysis, we see that each lap Dana walks around the track corresponds to an increase of 500 steps in the total number of steps she has taken.
Therefore, the rate of change for this relationship is:
**The total number of steps Dana has taken today increases by 500 steps for each lap around the track.**
From the data provided:
- From 2 laps (3,000 steps) to 4 laps (4,000 steps):
Change in steps = 4,000 - 3,000 = 1,000 steps
Change in laps = 4 - 2 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
- From 4 laps (4,000 steps) to 6 laps (5,000 steps):
Change in steps = 5,000 - 4,000 = 1,000 steps
Change in laps = 6 - 4 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
- From 6 laps (5,000 steps) to 8 laps (6,000 steps):
Change in steps = 6,000 - 5,000 = 1,000 steps
Change in laps = 8 - 6 = 2 laps
Rate of change = 1,000 steps / 2 laps = 500 steps per lap
From this analysis, we see that each lap Dana walks around the track corresponds to an increase of 500 steps in the total number of steps she has taken.
Therefore, the rate of change for this relationship is:
**The total number of steps Dana has taken today increases by 500 steps for each lap around the track.**