SOLUTION: Please help. In 1920, the record for a certain race was 45.4 sec. In 1960, it was 44.6 sec. Let R(t) = the record in the race and t= the number of years since 1920. a.)Find a

Question 179348: Please help.
In 1920, the record for a certain race was 45.4 sec. In 1960, it was 44.6 sec.
Let R(t) = the record in the race and t= the number of years since 1920.
a.)Find a linear finction that fits the data.
b.) Use the functionin (a) to predict the record in 2003 and in 2006.
c.) Find the year when the record will be 43.4 sec.
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
from 1920-1960 there is 40 years
:
the difference between 45.4-44.6=.8
:
that difference took place over a 40 year span so we have to divide the difference by 40 to get a yearly average of the change
:
.8/40=.02. this is how much on average per year that the race time is falling
:
equation: R(t)=-.02t+45.4
:
b)2003 would be 83 years:R(83)=-.02(83)+45.4=-1.66+45.4=43.74sec
2006 would be 86 years:R(86)=-.02(86)+45.4=-1.72+45.4=43.68sec
:
c)43.4=-.02t+45.4
:
-.02t=-2
:
t=100 years......so in the year 2020 this formula predicts a time of 43.4sec
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