Gold Medal Heights

Linear function (calculus)

Gold Medal Heights


The high jump has and always will be a sport of the Olympics. Athletes of the high jump push themselves harder and harder to achieve their best, physically possible jump height in preparation for competing in the Olympic games. With the use of the best–fit graph, this report will examine the high jumps over numerous Olympic years as well as for height predictions in the near future.

Below is the table of jump heights from the Olympic games between 1932 and 1980:

Year| 1932| 1936| 1948| 1952| 1956| 1960| 1964| 1968| 1972| 1976| 1980| Height (cm)| 197| 203| 198| 204| 212| 216| 218| 224| 223| 225| 236|

This graph demonstrates the relationship between the years (the x–axis) and the jump heights (the y–axis) of the gold medalists in the Olympic games between 1932 and 1980. If the actual value of the years were applied into the graph without any change, it would have been too spacious and complicated to present the data. Therefore, to make things simpler, I decided to remove each year’s first two digits.

e.g.) 1932 = 32

With the use of the formula y = mx + c, the parameters are m and c.

One constraint of this task is that two data points on the graph were removed from the regular pattern, meaning that two possible data points were eliminated that may have contributed with the data collection. This was due to World War I; two Olympics were cancelled (8 years) which negatively affected jump height improvement causing 1948’s gold medalist to have a lower jump height than 1936’s gold medalist. Another constraint is that there are no negative years (x > 0, y > 0).

The function that best models the behavior of the graph would be a linear function due to the fact that a best–fit line on the graphing program almost resembles a straight line. Therefore, as said earlier, I will be using the equation y = mx + c.

By manually drawing in a straight line that I believe best–fits the...
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