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4 April, 22:48

The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found a negative linear relationship between f and n that is best modeled by the equation f=-1.2n+38.1. What statement is true? The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes. The model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 1.2 minutes.

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Answers (2)
  1. 4 April, 23:04
    0
    Let's interpret this equation. If we have that a runner has 0 races under his belt, he completes the race in 38.1 min. We have that the slope is - 1.2 min/race and the intercept at n=0 is 38.1 min. Hence, for every race, the duration of the run decreases by 1.2 min (or increases by - 1.2 min).

    Lets derive that. Suppose a runner that has run n races, runs once more.

    The difference of times is:

    (-1.2 (n+1) + 38.1) - (-1.2n+38.1) = - 1.2 (n+1) - (-1.2n) = - 1.2n-1.2+1.2n=1.2 minutes.

    Hence, the correct answer is the first.
  2. 4 April, 23:15
    0
    The first thing we must do for this case is to define variables.

    n = number of 5k races covered

    f = end time.

    We have the following equation:

    f = - 1.2n + 38.1

    We note that the slope of the line is:

    m = - 1.2 minutes per race

    Therefore, the time decreases 1.2 minutes when the number of races increases n.

    Answer:

    The model predicts that for each additional race to runner has run, the finishing time decreases by about 1.2 minutes
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Home » Mathematics » The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found a negative linear relationship between f and n that is best modeled by the equation f=-1.2n+38.1.
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