preview

Math 30 IB Standard Level Body Mass Index Portfolio Assignment

Best Essays

This portfolio is an investigation into how the median Body Mass Index of a girl will change as she ages. Body Mass Index (BMI) is a comparison between a person's height (in meters) and weight (in kilograms) in order to determine whether one is overweight or underweight based on their height. The goal of this portfolio is to prove of disprove how BMI as a function of Age (years) for girls living in the USA in 2000 can be modeled using one or more mathematical equations. This data can be used for parents wanting to predict the change in BMI for their daughters or to compare their daughter's BMI with the median BMI in the USA.

The equation used to measure BMI is:

The chart below shows the median BMI for girls of different ages in the …show more content…

That can be fixed by adjusting the horizontal phase shift value of _c_ to 12.4 to compensate.

There is also a noticeable discrepancy between the function graph and the scatter plot in the domain {} and {}. A slight stretch about the y axis would fit the curve closer to the data points in those areas, therefore the _b_ value should be changed from π/15 to π/14. The number π/14 was chosen because reducing the denominator's value by 1 will increase the b value by a slight amount, and an increased b value will shorten period and compress the graph about the y axis, resulting in the values within domain to be closer to that of the data points.

Making these changes, the revised formula for the sinusoidal function is as follows:

Using TI InterActive!™ to graph that function, overlaid with the original data, and restricting the graph of the function to the same domain and range as the domain and range on the scatterplot, the graph is as follows:

The refined equation fits the data much more closely at the beginning, yet around the Age = 13 mark it starts to deviate again. Looking at this graph, one can come to the conclusion that it will take more than one mathematical function to graph the entirety of the data.

If one were to relate the concept of human growth with the measurable

Get Access