In 1920, the record for a certain race was 46.7 sec. In 1950, it was 46.4 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) Use the function in (a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be 45.80 sec.

Find a linear function that fits the data.
R(t)= ???

Question

In 1920, the record for a certain race was 46.7 sec. In 1950, it was 46.4 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) Use the function in (a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be 45.80 sec.

Find a linear function that fits the data.
R(t)= ???

anonymous · Answer

R(t) = 46.7 - 0.3/30t
R(t) = 46.7 -0.01t

yr 2003

R(t) = 46.7 - 0.01* 83
      =  46.7 - 0.83
      =   45.87

yr 2006    R(t) = 46.7 - 0.86 = 45.84

45.80 = 46.7 - 0.01t
t = ( 46.7 - 45.8)  / 0.01
  =  0.9 / .01 =  90

yr = 1920 + 90  = 2010