Aim: The aim of this task is to consider the winning height for the men’s high jump in the Olympic Games.
The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games.
Year |
1932 |
1936 |
1948 |
1952 |
1956 |
1960 |
1964 |
1968 |
1972 |
1976 |
1980 |
Height(cm) |
197 |
203 |
198 |
204 |
212 |
216 |
218 |
224 |
223 |
225 |
230 |
Note: The Olympic Games were not held in 1940 and 1944.
Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly. Discuss any possible constraints of the task.
What type of function models the behaviour of the graph? Explain why you chose this function. Analytically create an equation to model the data in the above table.
On a new set of axes, draw your model function and the original graph. Comment on any differences. Discuss the limitations of your model. Refine your model if necessary.
Use technology to find another function that models the data. On a new set of axes, draw both your model functions. Comment on any differences.
Had the Games been held in 1940 and 1944, estimate what the winning heights would have been and justify your answers.
Use your model to predict the winning height in 1984 and in 2016. Comment on your answers. The following table gives the winning heights for all the other Olympic Games since 1896.
Year
|
1896 |
1904 |
1908 |
1912 |
1920 |
1928 |
1984 |
1988 |
1992 |
1996 |
2000 |
2004 |
2008 |
Height
(cm)
|
190 |
180 |
191 |
193 |
193 |
194 |
235 |
238 |
234 |
239 |
235 |
236 |
236 |
How well does your model fit the additional data? ?
Discuss the overall trend from 1896 to 2008, with specific references to significant fluctuations.
What modifications, if any, need to be made to your model to fit the new data?