SOLUTION: In 1920, the record for a certain race was 45.9 sec. In 1950, it was 45.0 sec. Let R(t)= the record in the race and t= the number of years since 1920. Find a linear function that

Question 145581: In 1920, the record for a certain race was 45.9 sec. In 1950, it was 45.0 sec. Let R(t)= the record in the race and t= the number of years since 1920.
Find a linear function that fits the data.
R(t)=
(round to the nearest hundredth)
What is the predicted record for 2003?
(Round to the nearest 10th)
What is the predicted record for 2006?
(Round to the nearest 10th)
Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In 1920, the record for a certain race was 45.9 sec.
In 1950, it was 45.0 sec.
Let R(t)= the record in the race and t= the number of years since 1920.
Find a linear function that fits the data.
You are given the "y-intercept" as (0,45.9)
Find the slope:
slope = (45-45.9)/30 = -0.9/30 = -0.03
EQUATION:
R(t)= -0.03t + 45.9
----------------------------
What is the predicted record for 2003?
t = 83 in 2003
R(83) = -0.03*83 + 45.9
R(83) = 43.41
---------------------
What is the predicted record for 2006?
t = 86 in 2006
R(86) = -0.03*86 + 45.9
R(86) = 43.32
====================
Cheers,
Stan H.

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