in 1920, the record for a certain race was 45.8 sec. In 1980, it was 44.6 sec. Let R(t)=the record in the race and t=the number of years since 1920.

Question

find the linear function that fits the data
use the function (a) to predict the record in 2003 and in 2006
find the year when the record will be 43.84 sec.

R(t)=?
what is the predicted record for 2003? sec

what is the predicted record for 2006? sec

In what year will the predicted record be 43.84 seconds?

Answer 1

Check my thinking on this.
1920 to 1980 = 60 years.
In 60 years the record decreased by 45.8-44.6 seconds = 1.2 seconds or 1.2/60 = 0.02 sec/year.
Therefore, R(t) = 45.8-years83((0.02).
For 2003, that is 2003-1920 = 83 years.
R(2003) = 45.8 - 83(0.02)= ??

2006 is done similarly.
For the last part,
43.84 = 45.8-years(0.02) and solve for years.
Again, check my thinking.