Question

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.
2003 =
2006 =
c) Find the year when the record will be 46.68 sec.

Answer 1

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:
-1.2/60
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