the table shows the relationship between time spent running and distance traveled. running distance over…

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

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

Answer

Answer:

A. linear, because the r - value for the linear model is closest to 1

Explanation:

Step1: Recall model - type criteria

A linear model has a constant rate of change and a high correlation coefficient (r - value close to 1 or - 1). An exponential model has a non - constant multiplicative rate of change.

Step2: Analyze rate of change

For the given data: When time changes from 1 to 2 minutes, distance changes from 530 to 1050 feet. The change in distance $\Delta d_1=1050 - 530 = 520$ feet. When time changes from 2 to 3 minutes, distance changes from 1050 to 1600 feet. The change in distance $\Delta d_2=1600 - 1050 = 550$ feet. Since the rate of change is not exactly constant, we rely on the r - value. A high r - value (close to 1 for a positive linear relationship) indicates a good fit for a linear model. In general, an r - value close to 0 for an exponential model means it is not a good fit, and we expect a non - constant multiplicative rate of change for an exponential model which is not the case here. So, a linear model is appropriate because the r - value for the linear model is closest to 1.