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Question

In 1930, the record for the 1500-m run was 3.85 minutes. In 1950 it was 3.70 minutes. Fit a linear function to the points. Use the function to predict the record in 2006; in 2021.

Answer 1

1. Calculate the slope

m= Δy/Δx

m=(3.85-3.70)/(1930-1950)

m= -0.15/20

m=-3/400

Now the equation of the fit line

y-y0=m(x-x0)

y-3.7=-3/400(x-1950)

y=3.7+14.625-3x/400

y=18.325-3x/400

Then to find y at x=2006

y=18.325-3*2006/400

y=3.28

The record in 2006 is expected to be 3.28 min