Question

The first Olympics competition where women were allowed to compete in the 100 meter race was the 9th Olympiad in Amsterdam, the Netherlands, where Betty Robinson of USA won the gold medal with a time of 12.2 seconds. The current women’s world record for 100 meters was set in the 24th Olympiad in Seoul, Korea, where Florence Griffith-Joyner (Flo-Jo) finished in 10.49 seconds.

a. If the 9th Olympiad is our starting Olympiad, that means we can express the 100 meter race data for the 9th Olympiad as as P0 = 12.2 seconds. Using similar thinking, how would we express the 100 meter race data for the 24th Olympiad?

b. Use this data to create an explicit linear model for the women’s winning times for the 100 meters.











c. Use your model to predict the women’s winning time for the 100 meter race in the 50th Olympiad (assuming we all survive the zombie apocalypse and have a 50th Olympiad).  

Answer 1

Solution -

Given -

a)    For 9th olympiad

So for 24th olympiad

b) We have two points (0,12.2) and (15, 10.49)

Slope of line

Using slope intercept form y = mx+b

Here t is time in seconds and n is number of olympiads after 9th olympiads .

C) For 50th olympiad

n = 50-9 = 41

seconds