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IB Math SL type II Portfolio - Body Mass Index

Extracts from this document...

Introduction

MATHEMATICS INTERNAL ASSESMENT

SL TYPE II

Body Mass Index

Escaan International School

18/10/2012

BODY MASS INDEX

In this investigation, I will analyse various functions using the data given. A model function will be reached in base with this real-life 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.

 Age BMI 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65

(Source: http://www.

Middle

The behaviour of this graph can be modelled by the sine function

, or by the cosine function

as it is periodic and ondulating, which means it repeats a pattern as it goes up and down. Other functions can’t be used in this model as the information given can be reflected in other type of graphs. Finally, we can deduce that it will be a cosine function as the portion that we observe in tha graph doesn’t go through the origin (0,0), as the sine function would do.

After deducing which function type best fits the provided data, I used a GDC to test different forms of

through trial and error and found that the function

modeled the data closely, although a few values didn’t exactly fit the data.

Conclusion

"1" rowspan="1">

3

15.80

4

15.30

5

15.20

6

15.30

7

15.30

8

15.60

9

16.00

10

16.40

11

17.30

12

18.00

13

18.30

14

19.00

15

19.40

16

20.20

17

20.50

18

21.00

19

21.30

20

21.40

When graphed:

The model function

does not fit exactly over this data.

In order to make it fit, the function would need to be redefined in order to make the curve fit better.  After using trial and error and manipulating the model function I came up with a new function that matched the information a bit better. It is graphed below:

The function that I came up with and that matches much better the data is:

. It is very similar to the model function of before, but I have altered the horizontal translation slightly so that it matches better.

LIMITATIONS

-Values for x and y can’t be negative as it is a real-life example.

-The model function for American women doesn’t fit with French women as bmi changes slightly.

-The correlation doesn’t make a perfect line so the function is not 100% accurate.

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

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