Question 257686
In 1920, the record for a certain race was 45.4 sec. In 1990, it was 44.7 sec. Let R(t) = the record race and t = number of years since 1920.
In what year will the predicted record be 44.50? 
:
I think there is a slight inaccuracy in the equation you came up with
:
The slope: m = {{{(44.7-45.4)/(70 - 0) }}} = {{{(-.7)/70}}} = -.01
The equation should be:
 f(t)= -.01t + 45.4; where t is the years from 1920
then
2003: t=83
f(t) = -.01(83) + 45.4
f(t) = 44.57
and the same way:
2006: t=86
f(t) = 44.54
:
Find the year when it's 44.50; find t when f(t) = 44.5
-.01t + 45.4 = 44.5
-.01t = 44.5 - 45.4
-.01t = -.9
t = {{{(-.9)/(-.01)}}}
t = +90 yrs
:
1920 + 90 = 2010 the year for a record of 44.5 seconds