Question

the table shows the relationship between time spent running and distance traveled. which type of model best describes the relationship? running distance over time time (minutes) distance (feet) 1 530 2 1,050 3 1,600 4 2,110 5 2,650 linear, because the r value for the linear model is closest to 1 exponential, because the rate of change between each pair of points is 1.98 linear, because the rate of change between each pair of points is exactly 520 exponential, because the r value for the exponential model is closest to 0

Explanation:

Step1: Calculate rate of change

For time from 1 - 2 minutes: $\frac{1050 - 530}{2 - 1}=520$

Step2: Calculate other rate - of - changes

For time from 2 - 3 minutes: $\frac{1600 - 1050}{3 - 2}=550$
For time from 3 - 4 minutes: $\frac{2110 - 1600}{4 - 3}=510$
For time from 4 - 5 minutes: $\frac{2650 - 2110}{5 - 4}=540$

Step3: Analyze the model

The rates of change are approximately constant, suggesting a linear model. Also, in a linear relationship, the rate of change (slope) between points is relatively stable. And a high $r$ - value (close to 1 or - 1) for a linear regression indicates a strong linear relationship. Here, the approximate constancy of the rate of change points to a linear model.

Answer:

linear, because the rate of change between each pair of points is approximately constant