SOLUTION: in the 1920 the record for a certain race was 46.3 sec. in 1930 it was 46.1sec. let R(t)= the record in the race and t= the number of years since 1920 . a)find a linear functi

Question 407537: in the 1920 the record for a certain race was 46.3 sec. in 1930 it was 46.1sec. let R(t)= the record in the race and t= the number of years since 1920 .

a)find a linear function that finds the data
b)use the function in a) to predict the record in 2003 and 2006
c)find the year when the record will be 44.50
Answer by graphmatics(170) (Show Source): You can put this solution on YOUR website!
The decrease in sec of race speed reduction of t years is,
f(t) = (46.3-46.1)*(t/10)
f(t) = 0.2*(t/10)
f(t) = 0.2*t/10
f(t) = 0.2*t/10
___________________________________________________
so for 2003
f(2003-1930) = 0.2*((2003-1930)/10))
f(t) = 1.46 secs will be the decrease, so the record speed is
46.3 - 1.46 = 44.84
___________________________________________________
To find the year when the record will be 44.50
46.3 - f(t-1930) = 44.50
-f(t-1930) = 44.50 - 46.3
-f(t-1930) = -1.8
f(t-1939) = 1.8
0.2*(t-1930)/10 = 1.8
0.2*t = 18 + 0.2*1930
t = (18 + 386)/0.2
t = 2020
RELATED QUESTIONS
In 1920, the record for a certain race was 45.7 sec. In 1980, it was 43.9 sec. Let R(t)=... (answered by richwmiller)

In 1920, the record for a certain race was 45.7 sec. In 1990, it was 44.3 sec. Let R(t)=... (answered by ankor@dixie-net.com)

In 1920, the record for a certain race was 46.6 sec. In 1940 it was 46.2 sec. Let R(t)= (answered by drk,richwmiller)

In 1920, the record for a certain race was 45.8 sec. In 1959, it was 44.9 sec. Let R(t)=... (answered by drk)

In 1920 the record for a certain race was 45.1 sec. In, 1980, it was 4303 sec. Let R(t)= (answered by ewatrrr)

In 1920, the record for a certain race was 45.1 seconds. In 1950, it was 44.8 seconds.... (answered by nerdybill)

in 1920, the record for a certain race was 46.9 sec. in 1940, it was 46.5 sec. Let R(t)=... (answered by stanbon)

In 1920, the record for a certain race was 45.1 sec. In 1970, it was 44.1 sec. Let... (answered by ankor@dixie-net.com)

In 1920, the record for a certain race was 46.8 sec. In 1980, the record was 45.6 sec.... (answered by mangopeeler07)