# Portfolio: Body Mass Index

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Introduction

Mathematical Portfolio

Task II:

Body Mass Index

Vesela Germanova Germanova

The data given in the task is plotted in the following graph:

The values on the x-axis express the age and the values of the y-axis – the Body Mass Index. As far the age of a person must be always a positive number, than the BMI must also be a number bigger than 0.

The graph of the function behaves like a Gaussian function. The Gaussian function has a general expression of this look:

,

where a, b, c are bigger than 0,

and e ≈ 2.718281828 (Euler's number).

I chose this function, because the curve line, that the Gaussian function forms fits the best to the graph I got from the data for the age of females and their BMI.

Middle

The black line represents the equation y, where:

A = 18,81

B = -1,591

C = 0,2069

D = -0,007266

E =

F = 9,787

Before using this equation for a model, it is better first to test it. Using the graphical calculator I calculated the BMI of a 2-year-old girl. This is what I got:

The answer (16.398) is very close to real BMI of a 2-year-old girl, which is 16.40. This little testing gives me the courage to proceed with the task and to estimate the BMI of a 30-year-old woman in the USA using my model. The result is as follows:

The result looks relatively fine, because it is near to the quantity of the BMI of a 20-year-old woman and during that period of time (between 20 to 30-35 years)

Conclusion

15.43

7

15.38

8

15.43

9

15.62

10

15.98

11

16.54

12

17.29

13

18.18

14

19.13

15

20.03

16

20.78

17

21.29

18

21.56

19

21.63

20

21.62

The graph, which represents this data, is:

My model does not perfectly fit this data, but using the same method, but with the different quantities one will develop another model, with different coefficients, which would fit this data better. Anyway, this model has limitations, because every race has different characteristics, including differences in weight, height, etc.

List of sources:

http://www.nhlbisupport.com/bmi/bmi-m.htm (March, 2009)

http://www.scielo.br/img/revistas/jped/v82n4/en_a07tab01.gif (March, 2009)

Owen, John. Haese, Robert. Haese, Sandra. Bruce, Mark. “Mathematics for the international student”, Haese and Harris publications

TI-84 Plus Silver Edition

Graphic Analysis 3.4 Demo Version

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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