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

4

6

8

3,000

4,000

5,000

6,000

Describe the rate of change for this relationship.

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The total number of steps Dana has taken today

by per

lap around the track.

Answer 1

To describe the rate of change for the relationship between the number of laps Dana completes and the total number of steps she has taken, we need to look at the change in the number of steps corresponding to the change in the number of laps.

From the data provided:

- At 2 laps: 3,000 steps
- At 4 laps: 4,000 steps
- At 6 laps: 5,000 steps
- At 8 laps: 6,000 steps

We can see that when Dana increases the number of laps by 2, her total steps increase by 1,000.

To calculate the rate of change:

1. **Change in steps**: 1,000 steps (from 3,000 to 4,000 when increasing from 2 laps to 4 laps)
2. **Change in laps**: 2 laps

So, the rate of change in total steps per lap around the track can be calculated as:

\[
\text{Rate of change} = \frac{\text{Change in steps}}{\text{Change in laps}} = \frac{1,000 \text{ steps}}{2 \text{ laps}} = 500 \text{ steps per lap}
\]

Therefore, the rate of change for this relationship is that the total number of steps Dana has taken today **increases by 500 steps per lap around the track.**