• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

IB SL Math Portfolio- Body Mass Index

Extracts from this document...

Introduction

SL PORTFOLIO TYPE II
“Body Mass Index”

BODY MASS INDEX

Throughout this portfolio, various functions will be evaluated, applying the given data.
A model function will be determined and extrapolated as it relates to the following real-world example:

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

The table below provides the median BMI for females of varying ages in the US in the year 2000.

 Age (yrs) BMI 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65

(Source: http://www.cdc.gov)

When graphed: (The independent variable being the age of the women studied <x>, and the dependent being the BMI of these women <y>. Both values must always be greater than zero. )

This graph’s behavior is most nearly modeled by the cosine function,  , because it is undulating and periodic: it repeats a pattern as it rises and falls. However, due to the limitations presented by the nature of the given information itself, only the portion of the

Middle

through trial-and-error, and decided that the function
f(x) =3cos(.2x-4)+18most closely modeled the data, though certain values did not perfectly correlate. Below is a graph showing both the given BMI data and this model cosine function, for comparative purposes. It can be seen that the actual raw data very nearly coincides with the model: they curve in a relatively similar fashion, for example. The graphs are not, however, identical. Certain points do not exactly line up with this model. The first few, for instance, before age five, have slightly higher x-values than the cosine model, as do the last few, after age sixteen. Other values also do not correlate perfectly. Nonetheless, the model illustrates the provided BMI statistics with relative accuracy. In order to discover a different function that models the given information, I used technology.  I downloaded Graph 4.3, and saved the given data, the cosine function, and the model function into the program. When I compared the graph of the BMI statistics with my own model, I noticed that they did not look as

Conclusion

to be a bit of a closer match. Below is the data graphed with this new model function, for comparative purposes. It can be observed that this model does not perfectly correlate with the data, but does reflect its trends with relative accuracy.  Because the data for Guatemalan women was more sporadic than the data for American women, it was much more difficult to discover a model that fit. In other words, the data did not always follow a consistent undulating pattern, while the first set did, making it harder for a function to correspond. There was also less data present, as there is a gap between ages seven and eleven and it stops at age eighteen, which also made it difficult to view any trends. The data often shows slightly higher x-values than the model, and at some points, they are lower.  Because I used a trial-and-error method (on both a GDC and the program Graph 4.3) to discover it, the model function I found may have somewhat limited accuracy, though it does illustrate the trends this data presents pretty closely. The function, while not a perfect match, is appropriate considering the limitations presented by the data itself.

http://www.hughston.com/hha/a_15_2_4.htm

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

Related International Baccalaureate Maths essays

1. This portfolio is an investigation into how the median Body Mass Index of a ...

Using those values, the range of a curve fitted to this data should be: {} Judging from the distribution of data, the pattern created looks very much like that of a sinusoidal function. Based on this assumption, Finding the values of a, b, c and d in the function should result in a graph that fits the data points.

2. Extended Essay- Math

9ï¿½-ï¿½ï¿½"pï¿½:ï¿½ï¿½ï¿½&yï¿½{ï¿½ï¿½(tm)ï¿½(ï¿½ï¿½ï¿½9ï¿½ï¿½ d^ï¿½ï¿½*"d...ï¿½...ï¿½#ï¿½ï¿½"Z-ï¿½\$ï¿½G1/4kBSï¿½ï¿½dï¿½ï¿½Tï¿½1/2ï¿½iï¿½(tm)"ï¿½ï¿½ï¿½9ï¿½ï¿½"ï¿½LÏï¿½78ï¿½sï¿½ï¿½`ï¿½ï¿½qï¿½ï¿½Kï¿½ï¿½'Jmï¿½-Vï¿½Wï¿½(c)ï¿½?ï¿½ï¿½ï¿½`uwíºï¿½"Fjï¿½ï¿½-X.ï¿½1/2ï¿½Üï¿½3/4ï¿½ï¿½ï¿½Þï¿½ï¿½4ï¿½ï¿½ï¿½,ï¿½_;ï¿½2ï¿½=ï¿½xtï¿½)ï¿½(tm)ï¿½ï¿½#"ï¿½^{Lï¿½Ng(ï¿½]ï¿½ b_ï¿½_UK1/4ï¿½eß¸Wï¿½Vï¿½ï¿½T~nlï¿½myï¿½ï¿½ï¿½ï¿½YV4(Aï¿½ ï¿½AxHrï¿½R jï¿½ï¿½_ï¿½9`C8>ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Mï¿½PCï¿½uï¿½ï¿½]ï¿½ï¿½Eï¿½`\$1Lï¿½1-ï¿½5ï¿½ï¿½ï¿½ï¿½8Kï¿½Qï¿½^ï¿½ p ï¿½44gï¿½4ï¿½Dï¿½,ï¿½ï¿½C'ï¿½ï¿½:]1/2*}'ï¿½-ï¿½ï¿½F}N /3e333×³ï¿½<gï¿½gcfkcï¿½ï¿½9ï¿½8Ý¹\7ï¿½c[ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½<*ï¿½-ï¿½\$B#ï¿½^ï¿½Oï¿½V<O"Vï¿½Gï¿½^ï¿½DF[VMNE^UASï¿½Pï¿½Fyï¿½J"j(r)Zï¿½ï¿½#ï¿½--eï¿½Hï¿½ï¿½ï¿½ï¿½9ï¿½cï¿½b&ï¿½"ï¿½ZU-ï¿½ï¿½v6Eï¿½ï¿½wmï¿½ï¿½:ï¿½;ï¿½rzï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½*ï¿½ï¿½1/4ï¿½1/4E|b)7|ï¿½ï¿½uï¿½{ï¿½ T-ï¿½sï¿½"ï¿½ï¿½5'ï¿½ï¿½1qï¿½{^\$ï¿½'ï¿½ï¿½ï¿½Lï¿½(tm)ï¿½(tm)ï¿½ï¿½1ï¿½%ï¿½ï¿½1/4olï¿½|nï¿½ï¿½/yï¿½ï¿½ï¿½×ï¿½ï¿½=ï¿½zlï¿½Ð¸ï¿½ï¿½ï¿½\$ï¿½tï¿½\*ï¿½ï¿½\$3/4*ï¿½ï¿½ï¿½ï¿½u5Ìµyuï¿½ï¿½ 1/4ï¿½×lï¿½ï¿½['.ï¿½ï¿½3/4ï¿½ï¿½zï¿½Ý§cï¿½ï¿½ï¿½ î­*\{ï¿½3/4ï¿½~ï¿½ï¿½"ï¿½2(}(r)ï¿½=ï¿½8vï¿½(c)ï¿½30Qï¿½Bcï¿½ï¿½"oï¿½ï¿½1/4;ï¿½^kfaï¿½ï¿½1/4ï¿½Ç...ï¿½ï¿½ï¿½ï¿½XÜ¿tyyï¿½ï¿½Ü·ï¿½ï¿½ï¿½"J?ï¿½ï¿½ï¿½l\ï¿½ï¿½(c)3/4uï¿½-ï¿½%ï¿½3ï¿½ ï¿½ï¿½\$ï¿½X?jï¿½&`,ï¿½ ï¿½ï¿½ï¿½'ï¿½ï¿½e"ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½-@ï¿½ ï¿½ï¿½czï¿½5&ï¿½Kï¿½:`Ë±ï¿½p2ï¿½4ï¿½#1/4(> ï¿½-`Fï¿½B#LSId%ï¿½ eï¿½ï¿½ ï¿½'ï¿½ï¿½ï¿½ï¿½nï¿½[Ó¿Aï¿½ zï¿½&ï¿½ yï¿½(c)ï¿½Ùy(tm)ï¿½ï¿½ï¿½...ï¿½ï¿½ï¿½Ë¡ï¿½ï¿½"+ï¿½Ûï¿½ ï¿½ï¿½M3/4ï¿½1Hï¿½,ï¿½)ï¿½Fï¿½ï¿½iï¿½ï¿½bï¿½âï¿½(c)ï¿½kï¿½O2rdyiKdE)w"|Vï¿½Wwï¿½(ï¿½ï¿½fï¿½ï¿½ï¿½mï¿½[7ï¿½3l4&ï¿½"ï¿½>3ï¿½ï¿½ï¿½cem=aKï¿½ï¿½ï¿½ï¿½ï¿½Nï¿½\ ï¿½ï¿½ï¿½Wv_ï¿½ï¿½ï¿½Vï¿½Yï¿½ï¿½ï¿½- h ' (r) m-ï¿½ï¿½2ï¿½ï¿½ï¿½ ï¿½ï¿½&T'\$ï¿½IMJæd2gï¿½ï¿½ï¿½iï¿½ï¿½:ï¿½0ï¿½/:|ï¿½ï¿½ï¿½ï¿½xeoï¿½\ibï¿½l...Gï¿½Xï¿½ï¿½(c)ogï¿½jqï¿½ ï¿½}ï¿½wkh1/2ï¿½ï¿½ï¿½<Þ¢qï¿½ï¿½ï¿½Õkï¿½ï¿½ï¿½ï¿½;;ï¿½"oß¬1/4Eï¿½"ï¿½ï¿½kï¿½ï¿½"gï¿½'ï¿½ï¿½<X}6ï¿½~ï¿½ï¿½ï¿½ï¿½1ï¿½'ï¿½Æï¿½ï¿½{(r)ï¿½ï¿½pï¿½ï¿½+ï¿½ï¿½o^1/2ï¿½y->=2#ï¿½!iï¿½ï¿½1/4ï¿½ï¿½"O= [_ï¿½ï¿½\t_r_ï¿½ï¿½ï¿½ï¿½Mhï¿½ï¿½ï¿½{ï¿½jï¿½ï¿½ï¿½kY?ï¿½?Ï¬Ö£×on"oï¿½mï¿½mï¿½ï¿½|ï¿½%ï¿½Eï¿½jï¿½Zï¿½Vï¿½Nï¿½3/43/4cï¿½ï¿½@%Åï¿½@ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½<3/41/21/2^1/21/21/2Yï¿½ï¿½7ï¿½ï¿½ï¿½ï¿½ï¿½+vï¿½ï¿½ï¿½(tm)ï¿½Ét'ï¿½ï¿½ï¿½7ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½sï¿½cï¿½b pHYs ï¿½ï¿½ IDATxï¿½]}pWï¿½NH ...ï¿½"ï¿½\$RHAï¿½"vï¿½MIï¿½"8ï¿½ï¿½dj;ï¿½ï¿½PGjï¿½(c)vï¿½~eï¿½ Z&ï¿½hï¿½Guï¿½ï¿½?ï¿½ï¿½Nï¿½ï¿½È¨ï¿½ï¿½Lï¿½hï¿½"3ï¿½DFQi ï¿½ï¿½ï¿½R\$ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½~ï¿½ï¿½ï¿½8"ï¿½ï¿½ï¿½}ï¿½ï¿½sï¿½ï¿½psï¿½gï¿½VNLLTï¿½Hï¿½ï¿½ï¿½t\Aï¿½M*x-'ï¿½@B ï¿½ï¿½8ï¿½]ï¿½0.<ï¿½PHï¿½":ï¿½fFï¿½".ï¿½ ï¿½&:ï¿½ï¿½ï¿½ï¿½... ï¿½ ï¿½³ Eï¿½"Nï¿½ï¿½hvaHï¿½¸ï¿½lB ï¿½ï¿½8ï¿½]ï¿½0.<ï¿½PHï¿½":ï¿½fFï¿½".ï¿½ ï¿½xï¿½7Ö¬Yï¿½?#ï¿½Í¢-ï¿½(r)

1. Math IB SL BMI Portfolio

If a curve was fitted to this data, the domain should be: {}, those values being the lowest and highest ages given in the table of data. The lowest y-value on the scatter plot is the data point at 5 years (15.20 BMI); the highest y-value on the scatter plot is the data point at 20 years (21.65 BMI).

2. Investigating the Graphs of Sine Function.

If C was a negative number, the curve instead of moving horizontally to the left, would move to the right. If A was a fraction, the wave's amplitude would be A as well. We know that it would have a smaller amplitude than the base graph of y = sin x.

1. Math Portfolio: trigonometry investigation (circle trig)

graph so it is coincident with the y=3cos? graph; therefore, the values of maxima, minima, amplitude, period and frequency are the same as the y=3cos? graph. y= (-3) cos? Reflected through the x axis from the y=3cos? graph; therefore, the values of maxima, minima, amplitude, period and frequency are the same as the y=3cos? graph. y=2sin? y=-2sin? y=2sin(-?)

2. Investigating the Graphs of Sine Functions.

Graph of y= sin(x+1) Conjecture: (a) transformation of the standard curve y= sin x: Now I am varying x by adding or subtracting C units. There are no negative values in this function so there won't be any reflections of the standard graph. This time only the position will be affected in the way that y=

1. Type II Portfolio - BMI

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 on any differences. Refine your model if necessary. The blue dotted points are the data points from the table on the first page.

2. Body Mass Index

that fits the graph one has to find A, B, C and D. To find the amplitude (A) one has to subtract the minimum y-value from the maximum y-value. Then one must divide the result by 2 in order to find the half the distance between the two y-values. • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work 