The organizers of a 5k race surveyed runners about their finishing times ([tex]f[/tex]) and the number of previous races they had run ([tex]n[/tex]). The organizers found a negative linear relationship between [tex]f[/tex] and [tex]n[/tex] that is best modeled by the equation [tex]f = -1.2n + 38.1[/tex].

Which statement is true?

A. The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes.

B. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 1.2 minutes.

C. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes.

D. The model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes.

We are given the model

[tex]$$
f = -1.2n + 38.1,
$$[/tex]

where [tex]$f$[/tex] is the runner's finishing time (in minutes) and [tex]$n$[/tex] is the number of previous races. The key part to look at in this equation is the coefficient of [tex]$n$[/tex], which is [tex]$-1.2$[/tex]. This coefficient tells us that for each additional race (an increase of 1 in [tex]$n$[/tex]), the finishing time [tex]$f$[/tex] decreases by 1.2 minutes.

Thus, the true statement is:

[tex]$$\textbf{The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes.}$$[/tex]