Question 144527
In 1920, the record for a certain race was 45.4 sec.
In 1960, it was 44.6. 
Let R(t)= the record in the race and t= the number of years since 1920.
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a) Find a linear frunction that fits the data.
You have two points relating years since 1920 and race records:
The points are (0,45.4) and (40,44.6)
slope = (44.6-45.4)/(40-0) = -0.02
intercept = 45.4
EQUATION: record = (-0.02)(years since 1920) + 45.4
r = -0.02t + 45.4
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b) Use the function in (a) to predict the record in 2003 and in 2006.
r(2003) = -0.02(2003-1920) + 45.4
r(2003) = -0.02(83) + 45.4 = 43.74
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r(2006) = ?????
I'll let you do this following the same pattern as above.
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c) Find the year when the record will be 43.6 sec. 
43.6 = -0.02t + 45.4
-0.02t = -1.8
t = 90
year = 1920+90 = 2010
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Cheers,
Stan H.