Ib Math Sl Body Mass Index Portfolio

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IB Math SL Portfolio
Body Mass Index (Type II)
April 11th/2012

In this portfolio, there will be investigations on the topic of the relationship between females of different ages and their body mass index (BMI-a measure of one's body fat). Body mess index is calculated by taking one's weight (kg) and dividing by the square of one's height. ___________________________________________________________________________

While growing up, the rate of growth of weight and height varies. Therefore, as age grows BMI changes as well. Here is a table which shows the median BMI for females of different ages in the US in the year 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 |

In order to investigate the relationship between the ages and BMI, we can plot the data points on a graph.

On the graph above, there are two variables. The independent variable is ages. The dependent variable is BMI. Domain and range of the graph are limited because of the limited data. On the data table, there only presents data from females of age 2 to 20. Therefore, domain and range on the graph are restricted by the task. The parameter of the graph is that it only measures females from the United States. Also, in age one, BMI varies a lot depending on different food taken and original body mass. Therefore, measuring from age two is more accurate.

The type of function that the graph above resembles is sine function. Quadratic function was a reasonable guess because there is a lowest point on the graph and variable BMI is getting lower until it reaches the lowest point and turning to increase. However, the difference of BMI, after the lowest point in age 5, gets smaller and smaller. The curve line is slowly getting smooth. Therefore, the graph is more like a wave line which sine function models. Also, in a sine function, there are a maximum point and a minimum point. There is already one minimum point on the graph, and the graph is seemingly reaching a maximum point evidenced by the degression of radian of the curve line. Therefore, it is reasonable to believe that sine function models the behavior of the graph.

Now, after confirm the type of function the graph resembles, let the graph be represented by the general form of sine function as below: [pic]
In order to create an equation of sine function that fits the graph, a maximum point has to be estimated. Here is a table of differences of BMI values between ages: |Ages between (years)|Differences of BMI |

|2-3 |0.7 |
|3-4 |0.4 |
|4-5 |0.1 |
|5-6 |0.01 |
|6-7 |0.19 |
|7-8 |0.4 |
|8-9 |0.5 |
|9-1- |0.5 |
|10-11 |0.7 |
|11-12 |0.68 |
|12-13 |0.52 |
|13-14 |0.66...
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