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Female BMI

Extracts from this document...

Introduction

                Jeremiah Joseph

QUEENSLAND ACADEMY OF SCIENCE MATHS AND TECHNOLOGY

Mathematics IA

SL Type 2

Jeremiah Joseph

10/8/2009

image00.png


This Internal Assessment will investigate models of female BMI data. BMI is the measure of one’s weight to their height. To calculate a person’s BMI their weight is divided by the square of their height. Shown below is data for female BMI values in the US in 2000.

Age (years)

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

The data points shown above were graphed, the resulting graph is shown below.

image01.png

The variables that were used in the graph above were age and BMI. The independent variable, age, was placed on the x axis. Age is the independent variable because it is constant. The dependant variable, BMI, was placed on the y axis. BMI is the dependant variable because is varies, dependant on the age.

It is clearly shown in the graph above that the BMI of females in the US in 200 can be modelled using the equation y= A sin (Bx-c) + D. This is because the graph is shown to have the same characteristics of a sin graph.

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Middle

image27.png

However, the period of this graph is unknown. To find the period of the graph the equation shown below must be used.

image28.png

Where max = the maximum independent variable value and min = the minimum independent variable value. The maximum independent variable value = 20 and the minimum independent variable value = 5. These values were read of the data table, shown above, and then substituted into the equation, shown below.

image29.png

image02.png

With the period discovered, B can be calculated by substituting the period value into the equation, this is shown below.

image03.png

image04.png

To find out the constant, c, in the sin equation the equation, shown below, is used. C determines the horizontal shift that the graph is translated through.

image05.png

However, the Horizontal shift first needs to be determined. The horizontal shift can be calculated using the equation shown below.

image06.png

Where max = the maximum independent variable value and min = the minimum independent variable value. The maximum independent variable value = 20 and the minimum independent variable value = 5. These values were read of the data table and then substituted into the equation, shown below.

image07.png

image08.png

It is now possible to substitute this value into the equation to find c, this is shown below.

image09.png

image10.png

image11.png

It is now necessary to find the constant D to produce an accurate equation modelling the graph of Female BMI values. D controls the amount that the graph is shifted vertically.

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Conclusion

Limitations to the sin model include the wave like curve of the graph that the model creates. This is unrealistic as after the age 25 women’s BMI should not fluctuate like the sin model depicts. This is because after the age of 25 women do not grow anymore, this would provide a straight line graph after the age of 25; this is not what the sin model predicts.

Bibliography

http://www.nature.com/ijo/journal/v24/n9/fig_tab/0801371t2.html Date Accessed: 8/8/09

http://static.howstuffworks.com/gif/bmi-comparison.gif Date Accessed: 9/8/09

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