In 1920, the record for a certain race was 45.4 seconds. In 1980, it was 44.2 seconds. Let R(t) = the record in the race and t=the number of years since 1920.

Find the linear function that fits the data:
R(t) = ?
Record for 2003?
Record for 2006?

And in what year will the predicted record b e 43.64 seconds?

Question

In 1920, the record for a certain race was 45.4 seconds.  In 1980, it was 44.2 seconds.  Let R(t) = the record in the race and t=the number of years since 1920.

Find the linear function that fits the data:
R(t) = ?
Record for 2003?
Record for 2006?

And in what year will the predicted record b e 43.64 seconds?

a_clan · Answer

R(t)= 45.4 - 0.02t

for 2003, t= (2003-1920)=83
So, R(83) = 45.4 - 0.02*83 = 43.74

Similarly for 2006, t= 86