Chapter 4.6, Problem 18E

Throughout the twentieth century, the record time for the mile run steadily decreased, from $4$ minutes $15.4$ seconds in $1911$ to $3$ minutes $43.1$ seconds in $1999$. Some of the record times are given in Figure $4.156$.

a. Convert the given data to ordered pairs $\left(x,y\right)$, where $x$ is the number of years since $1990$ and $y$ is the time in seconds.

b. Draw a scatter diagram, find the equation of the line of best fit, and find the correlation coefficient.

Year	$1911$	$1923$	$1933$	$1942$	$1945$	$1954$
Time (min:sec)	$4:15.4$	$4:10.4$	$4:07.6$	$4:04.6$	$4:01.4$	$3:59.4$

Year	$1964$	$1967$	$1975$	$1980$	$1985$	$1999$
Time (min:sec)	$3:54.1$	$3:51.1$	$3:49.4$	$3:48.8$	$3:46.3$	$3:43.1$

Figure 4.156 Record times for the mile run.

c. Predict the record time for the mile run in the year $2020$.

d. Predict when the record time for the mile run will reach $3:30$.

e. Predict when the record time for the mile run will reach $0:30$.

f. On what assumption are these predictions based? If this assumption is correct, how accurate are these predictions?