posted by Liz on .
In 1920, the record for a certain race was 46.6 sec. In 1980, it was 45.4 sec. Let R(t)= the record in the race and t = the number of years snce 1920.
a) Find a linear function that fits the data R(t) =
b) Use the function in (a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be 46.68 sec.
From 1920 to 1980 is 60 years. The record was shortened by 1.2 seconds. The slope of the line is the rise over the run, or:
for t=0, R(t) = 46.6 so the y intercept is 46.6.
The format of a line is y = mx + b where m is the slope and b is the y intercept. So,
a) so the line would have the formula:
R(t) = -(1.2/60)t+46.6
b) substitute t=2003-1920 into part a and solve for R(t)
substitute t=2006-1920 into part a and solve for R(t)
c) substitute R(t) = 46.68 into part a and solve for t