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Math Portfolio- Body Mass Index

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Amrit Warraich

IB SL Math 11

May 18th 2009

This portfolio will consist of trigonometry and technology in order to represent the BMI of the females in the year 2000 for the US and the other country. Using technology, we will be able to plot the BMI of females in the year 2000 as a function where x is the age of the female in years and y is that age’s correspondent BMI.

The domain of the function will be D: 2≤x≤20 because we only have data for the females in the US between ages 2 and 20.

...read more.


In order to figure out the function of this graph we must first assess that it seems to be a sine curve as it begins around the middle of the minimum or maximum where as a cosine graph begins at the minimum or maximum and tangent graph has clear asymptotes which this does not. Therefore the equation of the line would be given by the following calculations:



Value of A




Value of B





Value of D



We can check the value of d by doing the following:


On a new set of axis, we will graph our found function next to our original plot and comment on any differences: (see graph paper 1)

Now that I can see out found function and our date plot next to each other, we can see there is indeed a horizontal shift. We will need to refine our equation.

We should calculate the minimum of the function we derived in order to finds its x-value.

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We will now look at the BMI’s of females in Scotland from the ages of 3 and 16 from years 1989-1991. The time and ages are different from the prior data we received but the representation is somewhat close to the year 2000 regarding the BMI in Scotland as well.

For analysis purposes, we will only look at the 97th percentile on the above data. Our model fits this data very slightly. If we try to fit a function on this graph, we would have to shift out sine graph so the minimum was close to x=3 (yrs) instead of 7, increase the initial amount (d) by about 1. Scottish female BMI between the ages 3 and 16 are similar to the American females BMI of between 5 and 20.

The model obviously has limitations for example, its actual values would not work in many other regions of the world, and the frequency may change due to possible eating habits and available food changes tremendously if we are to look art it from a global perspective. It is probable to say that our model could represent North America’s BMI at the greatest.

...read more.

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