Question 155358: In 1920, the record for a certain race was 46.8 sec. In 1980, the record was 45.6 sec. Let R(t) + the record in the race and t = the number of years since 1920.
a) find a linear function that fits the data.
b) What is the predicted record for 2003?
c) What is the predicted record for 2006?
In what year will the predicted record be 45.0 sec?
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! In 1920, the record for a certain race was 46.8 sec. In 1980, the record was 45.6 sec. Let R(t)= the record in the race and t = the number of years since 1920.
a) find a linear function that fits the data.
b) What is the predicted record for 2003?
c) What is the predicted record for 2006?
In what year will the predicted record be 45.0 sec?
R(t)=record
t=# years since 1920
In 1920, the record for a certain race was 46.8 sec.
R(0)=46.8
In 1980, the record was 45.6 sec.
R(60)=45.6
y=f(x)
y=mx+b
Points:
(0,46.8)
(60,45.6)
slope= (45.6-46.8)/(60-0)= -1.2/60 or -1/50
y=(-1/50)x + b.
46.8=(-1/50)0+b
46.8=b
a) find a linear function that fits the data.
f(x)=(-1/50)x+46.8
---------------------------------------------------------
b) What is the predicted record for 2003?
x=2003-1920
x=83
f(83)=(-1/50)83+46.8
f(83)=45.14
45.14
---------------------------------------------------------
c) What is the predicted record for 2006?
x=2006-1920
x=86
f(86)=(-1/50)86+46.8
f(86)=45.08
45.08
---------------------------------------------------------
In what year will the predicted record be 45.0 sec?
f(x)=45
(-1.2/60)x+46.8=45
(-1.2/60)x=-1.8
x=90
1920+90=2010
2010
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