### Mathematical Modelling of BMI for Men aged 2-20

Mathematical Modelling of BMI for Men aged 2-20

Body Mass Index

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Body mass index is a step of the comparative weight based on an single person’s tallness and mass. The aforesaid is calculated by taking the person ‘s organic structure mass divided by the square of their tallness

Body mass indexMass ( kilogram )

[ Height ( m ) ]2

 Age ( old ages ) BMI ( male ) 2 16.7 3 16.3 4 15. 6 5 15.4 6 15.3 7 15.7 8 15.8 9 16.3 10 16.6 11 17.6 12 17.9 13 18.6 14 19.3 15 19.8 16 20 17 21.4 18 21.9 19 22.4 20 23.1

The information taken was with mention to males belonging to upper socio-economic strata ( age 2-20 old ages )

Below is the graph stand foring the information.

General Information-

In the given graph, the age selected is represented in old ages. BMI is the dependent variable and Age is independent variable.

The graduated table selected in the graph is appropriate for the given informations as the points of the dependant variable are clearly seeable.

Analyzing the Graph

The outline of the graph in this graduated table is equal since the graph can be analyzed easy.

The tendency noticed is that the graph tends to lift ; as the age of the topics rises i.e. the age is straight relative to the BMI. Although, the generalisation is non consistent from age 2 to 7. At this scope, the BMI of the topics drops to a lower limit and so follows the general tendency observed for age 7 to 20.

Modeling

A multinomial map sooner a quartic map could be used to pattern the behaviour of this graph although the exponential rise in the BMI after the age of 20 old ages would do it invalid.

Another map that could be used to generalise the tendency is either a sine or cosine curve, which are periodic maps.

A periodic map could calculate the information if it was to go on indefinitely.

Therefore, to pattern the informations, a theoretical account utilizing sine curve will be found.

The general sine map gives the restricting factors to be found.

a wickedness ( bx+c ) + vitamin D

Where,

a- amplitude

b- period

c-horizontal interlingual rendition

d-vertical interlingual rendition

The chief axis of the general sine map is y=d

The period of the general sine map is2?

B

The current period is 2?

Gives the restricting factors to be found.

Finding the amplitude utilizing the given informations by deducting the highest BMI ( 23.1 at age 20 old ages ) to the Lowest BMI ( 15.3 at age 6 old ages ) ,

23.1 – 15.3 = 7.8 = amplitude

Therefore, the amplitude is so divided by 2 to happen the ‘a’ parametric quantity.

amplitude =7.8= 3.9

2 2

Next, the ‘d’ parametric quantity can be found utilizing the amplitude.

The lowest BMI ( 15.3 at age 6 old ages ) added to half the amplitude can be used to cipher the ‘d’ bound.

15.3 + 3.9 = 19.2

The current equation must be horizontally shifted to the right.

-3.9sin ( x ) + 19.2 ________ ( negative used in order to toss the sine curve )

Maximum of 1 rhythm ?3?

2

Minimum of 1 rhythm ?1?

2

Maximum of 1 rhythm – lower limit of 1 cycle=3?1?= ? ?3.14

2 2

The ‘b’ bound can be found by utilizing the upper limit and lower limit. Each rhythm of the theoretical account is about 3.14 ( ? )

Harmonizing to the given informations, a individual rhythm of the organic structure mass index of a female is near to 15 old ages. The current theoretical account can be stretched to run into that demand by multiplying ten by?. The current

15

theoretical account still does non fit the given graph adequately. To aline the current theoretical account, the degree Celsius parametric quantity must be found.

By taking any arbitrary point, a difference is found by utilizing the x-value as input for the current theoretical account. The horizontal displacement that is the ‘c’ restriction is hence the difference found.

Given point= ( 11, 17.6 )

Horizontal displacement = 17.669 – 17.49 = 0.0.179=d

And therefore the equation formed is-

Comparing the original informations to the revised information ( the new theoretical account )

The original information points are represented as purple filled circles whereas the ruddy line represents the theoretical account created via the map. There are points like x=6, y=15.3 and x=8, y=15.8 that autumn on the theoretical account function’s curve. However there are besides points that do non fall on the curve and far from it like x=15, y=19.8 and x=17, y=21.4. a horizontal displacement to the right would rectify the divergence. However, it would do the points thatmake autumnon the curve to be re-aligned and hence, move farther off from the theoretical account curve.

The following tabular array contains the independent variable, age ( in old ages ) and the two dependent variables ( BMI- given and BMI- modeled ) the last column gives the difference in the BMI of the given informations and created theoretical account.

 Age ( old ages ) BMI ( Given informations ) BMI ( modeled ) BMI ( difference ) 2 16.7 17.00 -0.3 3 16.3 16.38 -0.08 4 15. 6 15. 88 -0.28 5 15.4 15.52 -0.12 6 15.3 15.33 -0.03 7 15.7 15.31 0.39 8 15.8 15.45 0.35 9 16.3 15.76 0.54 10 16.6 16.22 0.38 11 17.6 16.81 0.79 12 17.9 17.50 0.40 13 18.6 18.27 0.33 14 19.3 19.08 0.22 15 19.8 19.89 -0.09 16 20 20.67 -0.67 17 21.4 21.39 0.01 18 21.9 22.01 -0.11 19 22.4 22.51 -0.11 20 23.1 22.87 0.23

The difference in both the BMI shows how close the theoretical account is to the given informations. The largest and the smallest difference viz. 0.79 and 0.01 severally are comparatively little. Taking the norm of all the BMI ( difference ) , the value obtained is 0.0973, which is moderately close to zero.

Using the norm to polish the current theoretical account,

The mean difference in BMI can be used to cipher the new ‘d’ parametric quantity.

Therefore,

0.179+ 0.0973 =0.2763

A minimal and maximal bound is hence developed which is needed to aline the current theoretical account.

Taking the norm of the Numberss, we get

0.179+ 0.2763= 0.22765

2

0.22765 is the new ‘c’ parametric quantity

Therefore, the new equation found is,

Analyzing the graph

The green solid line appears to be closer to the given informations points than the ruddy flecked lines. The line appears to be closer in the initial ( 4-6 old ages ) and the concluding ( 13-20 old ages ) than the one shown in the old theoretical account.

Besides, The norm of the recreated theoretical account is closer to zero than that of the old theoretical account turn outing that the recreated theoretical account is so, a more suited theoretical account for the information collected.

Hence, a map that theoretical accounts the given male informations has been computed, revised, rectified and presented via graphs. The theoretical account has been tested utilizing following illustrations and is been found to be near to preciseness. The restrictions and bars of the theoretical account has been discussed and explained further.

The revised theoretical account is periodic, so it could theoretically be used to happen the organic structure mass index of person older than 20 and still be slightly relevant unlike in the quartic map.

To prove this theory, a random age is picked and the BMI is calculated.

Taking the BMI of a newborn babe by puting the x-limitation to zero,

We get 18.319, which is sensible due to the individual’s little tallness and rather a spot of weight.

Calculating the BMI for an 85 twelvemonth old male,

We get 22.05.

The reply is sensible since at old age, a 85 twelvemonth old adult male would thin out and go a small shorter and so the BMI would be less than that of a healthy 30 twelvemonth old male.

Restrictions of the revised theoretical account

One of the biggest restrictions of the theoretical account is the range of truth. Although the theoretical account maps good for the age group between 2-20 twelvemonth old, and has a graduated table that maps good, it is improbable that the informations will be near to truth due to the theoretical account being found by manus. And hence the restriction is that theoretical account maps created by manus are hard to be perfected.

Another restriction to the theoretical account is the inclusion of negative values. Negative values are impossible as an person can non hold negative tallness or weight and hence a negative BMI. This could be prevented by restricting the sphere to forestall negative values.

The values chosen were comprised of values that are average for the males falling in the 50Thursdaypercentile. The restriction in the informations could easy make an off-curve informations point, which would intend that the revised theoretical account would be irrevelant.

Decision

Hence, a map that theoretical accounts the given male informations has been computed, revised, rectified and presented via graphs and computations. The theoretical account has been tested utilizing illustrations and is been found to be near to preciseness with accounts measuring the information obtained. The restrictions and bars of the theoretical account has been discussed and explained.

Bibliography

“ IB Mathematics / Calculus Portfolios. ”Ryan Rampersads Chronicles. Ryan Rampersad, 2 Oct. 2010. Web. 15 Nov. 2014. & A ; lt ; hypertext transfer protocol: //chronicles.blog.ryanrampersad.com/2010/10/ib-mathematics-calculus-portfolios/ & A ; gt ; .

“ Desmos Graphing Calculator. ”Desmos Graphing Calculator. Desmos.Inc, n.d. Web. 12 Nov. 2014. & A ; lt ; hypertext transfer protocol: //www.desmos.com/calculator & A ; gt ; .

Matme/pf/m09/n09/m10/n10. “ The Portfolio. ”MATHEMATICS Standard Level( n.d. ) : n. pag. International Baccalaureate. Web. 15 Nov. 2014. & A ; lt ; hypertext transfer protocol: //ibopenacorada.files.wordpress.com/2009/12/d_5_matsl_tsm_0801_1_e.pdf & A ; gt ; .

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