## Number of Participating Nations in the Olympic GamesAnne di Vittorio

Rio, London, Beijing... How many countries participated?

The Olympics started in Greece, as a men only competition, and has now expanded to being an international event that happens every four years. Today, more "teams" participate in the Olympics than actual recognized independent countries. So, how many teams are there?

I found my data of the last 15 Olympics (1960 - 2016) on a website called Worldatlas. The countries go up every year, steeply at the beginning, and a little slower at the end because there are less countries that enter given most of them are already participating.

1960 - 1976
1980 - 1996
2000 - 2016
The Graph

I made a graph onĀ Desmos. We had to make a line of best fit for every five data points, and then a line of best fit for all the data. For the three lines, I made linear equations, but for the entire data, I made a logarithm.

The graph with just the data
The graph with every five data points has a line of best fit

Here are the calculations that I did on Microsodt OneNote 2010.

Line of best fit 1
Line of best fit 2
Line of best fit number 3

There are two outliers, (16,92) and (20,80). They were not taken into acount for the seperated and (full) line of best fit.

To find the line of best fit, I did a Logarithm. I played around with the numbers of the general rule (y = a log(x) +c) (because I do not know how to graph it), and then plugged those numbers into a rule.

Line of best fit where I played around (left)
Line of best fit with the real rule (top left - red)

My sister then also did it using the real math (not eyeballing) and a graphing calculator and found something similar to what I had found.

My sister's line of best fit (top left - orange)

Finally, we had to predict what it would look like in 2067 ( I did 2068 because that will be a year of an Olympic game) and in 2112. For both, I thought it would probably be around 210 countries, because we have reached more teams than recognized as independent countries (Taiwan is seen as part of China, but has its own team), and there aren't many more teams you can add... Which means that you can not follow the line of best fit because it goes a little too steep.

Thank You for you attention

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