Application on equations system.

Question

in 1930, the recored for 400-m run was 46.8 sec. in 1970, it was 43.8 sec. let R(t)=the record in the 400-m run and t= the number of years since 1930

a) find a linear function that fits the data.

b) use the function of part (a) to estimate the recored in 2003; in 2006.

c) when will the recored be 40 sec?

Answer 1

(a) Let R(t)=at+b where a and b are constants to be found.

At t=0 (that is, in 1930), R(0)=46.8, so b=46.8.

At t=40 (that is, in 1970), R(40)=43.8. So in 40 years the change was 43.8-46.8=-3 seconds.

The rate of change is -3/40, making a=-3/40.

R(t)=46.8-3t/40.

(b) For 2003, t=2003-1930=73, R(73)=46.8-73(3/40)=46.8-5.475=41.3 seconds approx.

R(2006-1930)=R(76)=46.8-76(3/40)=41.1 seconds.

(c) If R(t)=40, 46.8-t(3/40)=40, 3t/40=6.8, t=40×6.8/3=90.7 approx, corresponding to 1930+54.4=2020 (within the year).