Section 7.3B What does rate of change really tell us about 200-meter run records?

Section 7.3BWhat does rate of change
really tell us about
200-meter run
records?
World record times for the 200-meter run are listed in
the following table for various years.
1. Which gender’s record times are decreasing most on
average per year over the entire time frame? Use
calculations and words to explain.
2. Using the first and last points for both genders, find a
linear model for both the men’s and women’s
records over time, using 𝑥 = 0 for 1950.
a. Women’s: (23, 22.38), (38, 21.34)
b. Men’s: (1, 20.6), (59, 19.19)
Year
1951
1963
1967
1973
1974
1978
1979
1984
1988
1996
2009
Women’s
Record (Sec)
Men’s Record
(Sec)
20.6
20.3
20.14
22.38
22.21
22.06
19.72
21.71
21.34
19.32
19.19
3. What does the model predict the men’s and women’s records to be in 2015?
a. Women’s:
b. Men’s:
4. If the trends continue, in what year would you predict that the men’s and women’s record would be
equal?
5. A student says the men’s record times are decreasing the most per year because the decrease in their
record times from 1951 to 2009 is greater than the decrease in the women’s record times from 1973
to 1988. What would you tell the student?
6. A student uses the 1974 and 1978 data points to find a linear model for the women’s record times and
the 1963 and 1967 data points to find a linear model for the men’s record times. She finds that both
gender’s record times decreased by about 0.04 seconds/year. The student concludes that the record
times for each gender are decreasing at the same rate. What would you tell the student?