IB SL Math Portfolio- Body Mass Index

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“Body Mass Index”

BODY MASS INDEX                                

Throughout this portfolio, various functions will be evaluated, applying the given data.
A model function will be determined and extrapolated as it relates to the following real-world example:

Body mass index (BMI) is a measure of one’s body fat. It is calculated by taking one’s weight (kg) and dividing it by the square of one’s height (m).

The table below provides the median BMI for females of varying ages in the US in the year 2000.


(Source: http://www.cdc.gov)

When graphed:

(The independent variable being the age of the women studied <x>, and the dependent being the BMI of these women <y>. Both values must always be greater than zero. )

This graph’s behavior is most nearly modeled by the cosine function,, because it is undulating and periodic: it repeats a pattern as it rises and falls. However, due to the limitations presented by the nature of the given information itself, only the portion of the graph in the first quadrant that is positive applies, as both the age of the women and their respective body mass index values are real world examples and could never be negative. Other functions I experimented with, with the exception of the sine function, could not be used, because no portion of their graphs reflected the data provided. ( The sine function was another possible choice, but I found the cosine function to be adequate.) Below is a graph of the chosen function type,

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Once I had deduced which function type best fit the provided data, I used a GDC to test different forms of  through trial-and-error, and decided that the function
f(x) =3cos(.2x-4)+18 most closely modeled the data, though certain values did not perfectly correlate. Below is a graph showing both the given BMI data and this model cosine function, for comparative purposes. It can be seen that the actual raw data very nearly coincides with the model: they curve in a relatively similar fashion, for example. The graphs are not, however, identical. Certain points do not exactly ...

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