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 |\nwhich type of model best describes the relationship?\no linear, because the r value for the linear model is closest to 1\no exponential, because the r value for the exponential model is closest to 0\no linear, because the rate of change between each pair of points is exactly 520\no 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 |\nwhich type of model best describes the relationship?\no linear, because the r value for the linear model is closest to 1\no exponential, because the r value for the exponential model is closest to 0\no linear, because the rate of change between each pair of points is exactly 520\no exponential, because the rate of change between each pair of points is 1.98

Answer

Explanation:

Step1: Calculate rate of change

For a linear relationship, the rate of change (slope) between points should be constant. Calculate the differences in distance and time. For time from 1 - 2 minutes: Distance change = $1050 - 530=520$ feet. For time from 2 - 3 minutes: Distance change = $1600 - 1050 = 550$ feet. For time from 3 - 4 minutes: Distance change = $2110 - 1600=510$ feet. For time from 4 - 5 minutes: Distance change = $2650 - 2110 = 540$ feet. The rate of change is not exactly 520.

Step2: Analyze linear - r value concept

The $r$ - value (correlation coefficient) measures the strength and direction of a linear relationship. A value close to 1 or - 1 indicates a strong linear relationship. Without calculating the $r$ - value exactly, we can see that the data points seem to follow a linear trend more than an exponential one. In an exponential relationship, the ratio of consecutive $y$ - values should be constant. Here, the ratios are not constant.

Answer:

linear, because the $r$ value for the linear model is closest to 1