Question

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

running distance over time
\

$$\begin{tabular}{|c|c|} \\hline time (minutes) & distance (feet) \\\\ \\hline 1 & 530 \\\\ \\hline 2 & 1,050 \\\\ \\hline 3 & 1,600 \\\\ \\hline 4 & 2,110 \\\\ \\hline 5 & 2,650 \\\\ \\hline \\end{tabular}$$

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

Explanation:

Calculate rates of change

Using the Linear Rate of Change knowledge point

$$
LATEXBLOCK0
$$

Evaluate model options

Using the Linear Modeling knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) linear, because the \(r\) value for the linear model is closest to 1 (Correct answer)
• (B) exponential, because the \(r\) value for the exponential model is closest to 0
• (C) linear, because the rate of change between each pair of points is exactly 520
• (D) exponential, because the rate of change between each pair of points is 1.98