Let t be the year, and r(t) be the record for a given year.

We can define two points on the linear function we want.

(t0, r0) = (1920, 45.5)

(t1, r1) = (1930, 45.3)

Using these points, we can put them into the formula for the two-point form of the equation for a line.

(r - r0) = (r1 - r0)/(t1 - t0)*(t - t0)

r - 45.5 = (45.3-45.5)/(1930-1920)(t - 1920)

r = (-.2)/(10)(t - 1920) + 45.5

r(t) = -.02t + 83.9

The predicted record for 2008 is

(-.02(2008)+83.9 = -40.15+83.9 = 43.74) seconds

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In the year 4195, the winning runner is expected to teleport herself to the finish line in zero time.

We can define two points on the linear function we want.

(t0, r0) = (1920, 45.5)

(t1, r1) = (1930, 45.3)

Using these points, we can put them into the formula for the two-point form of the equation for a line.

(r - r0) = (r1 - r0)/(t1 - t0)*(t - t0)

r - 45.5 = (45.3-45.5)/(1930-1920)(t - 1920)

r = (-.2)/(10)(t - 1920) + 45.5

r(t) = -.02t + 83.9

The predicted record for 2008 is

(-.02(2008)+83.9 = -40.15+83.9 = 43.74) seconds

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In the year 4195, the winning runner is expected to teleport herself to the finish line in zero time.