In 1920, the record for a certain race was 45.7 sec. In 1970, it was 44.7 sec. Let R(t) = the record in the race and t= the number of years since 1920.
a- Find the linear function that fits the data
b- Use the function in (a) to predict the record for 2003 and in 2006
c- Find the year when the record will be 43.94 sec.

Question

In 1920, the record for a certain race was 45.7 sec. In 1970, it was 44.7 sec. Let R(t) = the record in the race and t= the number of years since 1920.
a-	Find the linear function that fits the data
b-	Use the function in (a) to  predict the record for 2003 and in 2006
c-	Find the year when the record will be 43.94 sec.

anonymous · Answer

a) Since the question asks for a linear function that gives us a hint that we want a straight line (y=mx+b). So you first need to find the slope:
m=(y2-y1)/(x2-x1)= (44.7-45.7)/(50-0)=-1/50=-0.02
Then we need to find our y-intercept (b), so we will use x=0 and y=50 which will represent the 1920 record:
50=-0.02(0)+b
50=b
Therefore, your linear function will be y=-0.02x+50
b) For the 2003 (2003-1920=83 years since 1920), plug in 83 for x. Likewise for the 2006 record plug in 86 for x.
c) Set y=43.94. So your equation looks like this:
43.94=-0.02x+50
Then solve for x:
(43.94-50)/(-0.02)=x