In 1920, The Record For Certain Race Was 45.5 Sec. In 1930, It Was 45.3 Sec. Let R(t)= The Record In The Race And T=the Number Of Years Since 1920. Can You Find The Linear Function That Fits The Data. R(t)=? Round To The Nearest Hundredth. What Is The Predic?

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.

In 1920, the record for a certain race was 45.5 sec. In 1940, it was 44.9 sec. Let R(t)= the record in the race and t= the number of years since 1920.

A) find a linear function tat fits the data.
B) Use the function in (a) to predict the record in 2003 and in 2006.
C) find the year when the record will be 42.86 sec.