Body mass index (BMI) is a measure of one’s body fat. It is calculated by taking one’s weight (kg) and dividing by the square of one’s height (m).

The table below gives the median BMI for females of different ages in the US in the year 2000.

(Source: )

Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly.

In the graph above, the variables shown are age in years and BMI. In this case,
the x axis is the age of the female in years and the y axis is the body mass index of the females.

The parameters are also known as the domain and range. The parameters of the plotted data are shown below:

The domain and range can also be seen clearly from the table. The x values range from 2 to 20, and the y values range from 15.2 to 21.65.

What type of function models the behavior of the graph? Explain why you chose this function. Create an equation (a model) that fits the graph.

Throughout this study, many different types of function models were experimented with. However, the one which models the behavior of the graph the best would be a sine function.

A simple sine function looks like:

Then this sine function would need to be manipulated to fit the data. This function was chosen because there is an obvious trend in the data that shows a curve. The sine function can easily be manipulated to fit the curve. The following equation shows how to manipulate the sine function:

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In this case all of the variables, which include a, b, c, and d would need to be manipulated to fit the data.

First, we must understand what each variable does:

Looking at the plotted data intimately and trying many different changes on the variables I came to the conclusion of:
a = 3
b = .2
c = -2.8
d = 18.5

Therefore, the equation would look like:

The equation above was graphed along with the plotted data and there was similarity between the two.

On a new set of axes, draw your model function and the original graph. Comment ...

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