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

Answer 1

consider 1920 --- > t = 0
then your given data can be represented by two ordered pairs
(0,46.6) and (60,45.4)

slope = (45.4-46.6)/(60-0) = - 0.02

R(t) = - 0.02t + b
sub in (0,46.6)
b = 46.6

R(t) = -0.02t + 46.6

now just plug in values of t corresponding to the years,
e.g. 2006 ---> t = 86
R(86) = -.02(86) + 46.6 = 44.88