# Plot a graph for the BMI of different females of different ages in the US in year 2000 and analyse whether it is an accurate source of data.

Body Mass Index _        Maths Coursework

March 2008 _                By:  12M(2)

This maths coursework is based on Body Mass Index. This is a measure of ones body fat; it is calculated by taking one’s weight (kg) and dividing it by the square of one’s height (m). For this coursework, I have to plot a graph for the BMI of different females of different ages in the US in year 2000 and analyse whether it is an accurate source of data and how it can help me to find other BMI’s around the world.

Below is my graph showing the BMI of different females of different ages in the US in the year 2000:

As shown on the graph, the ‘x’ values are the age of the females and the ‘y’ values are their body mass index. The age is measured in Years.

When modelling this data, the initial impression is to think that is was an f(x)= x2 graph. However once you notice that it is not a mere parabola but a wave due to the curve that levels off (shown on graph) we can assume it is a periodic function such as a cosine or sine graph. Even though you can use a cosine or a sine graph, I decided to use a cosine graph, as I am more familiar with this type of graph.

After inputting the cosine function into autograph software, you would realise that transforming the function would be appropriate so that it can model the graph more accurately. In order for you to do this, you have to use the general formula of f(x)= acos(bx + c) + d. This is because it enables you to transform the function. The function I found was: f(x)= 3.2cos(11x-230) + 18.5. The model is shown below:

When transforming the function, you have to understand the general formula stated above. In order to stretch the graph so that the wave would have the same amplitude; you have to use the function af(x) as it gives a vertical stretch. I put in 3.2 as it seemed appropriate. Then, to make my function wider and create a horizontal stretch by a factor of 1/b, I put 11 in front of the x. Once this was done, I ...