# models and graphs relating the Body Mass Index for females to their ages in the US in the year 2000

Anh Nhu Vu

IB

Mathemathics Standard Level 2008

Maths Coursework

This coursework will explore models and graphs relating the Body Mass Index for females to their ages in the US in the year 2000. The ages and the corresponding BMI numbers are variables and as we generate the function that models the behaviour of the graph later on, the parameters are the values of a, b, c and d in the formula of the function.

When the data points are plotted on a graph, it is interesting to see what kind of graph these points are forming.

The graph BMI appears to resemble the graph of a trigonometric function. If we base on the function y=sinx to develop our model function, the type of function that models the behaviour of the graph is:

y1=a×sin [b(x+c)] +d

These are the reasons why I chose this type of function:

Primarily, the shape of the graph resembles that of the graph of the function y=sinx.

However, in comparison to the graph of the function y=sinx, the data points of the graph BMI indicates that the processes of transformation have been done:

_Vertical and horizontal stretch (the scales are represented by a and b)

_Vertical and horizontal translation (the scales are represented by c and d)

Once we have indentified the type of the function that models the behaviour of the graph, it is possible to use algebraic methods to create an equation that fits the graph BMI.

_Consider the graph of the function y=sinx

The distance from a point where y= -1 (the minimum value) to the nearest point where y=1 (the maximum value) is.

According to the graph BMI, we can see that the point (5; 15.2) represents the minimum value of the graph if it is to resemble the shape of the graph y=sinx. Even though there is a possibility that the graph BMI will extend further than the point (20; 21.65), in which case its maximum point is not shown on the graph BMI, we come to a hypothesis that the point (20; 21.65) represents the maximum value ...