Math 30 IB Standard Level Body Mass Index Portfolio Assignment Essay Sample

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Using those values. the scope of a curve fitted to this information should be Judging from the distribution of informations. the form created looks really much like that of a sinusoidal map. Based on this premise. Finding the values of degree Celsius and vitamin D in the map should ensue in a graph that fits the information points.Assuming that the point 21. 65 is the upper limit of the sinusoidal curve and utilizing 15. 20 as the lower limit. one can happen the value for vitamin D utilizing the expression:vitamin D = 18. 425vitamin D = 18. 4

The line of symmetricalness in a sinusoidal map is equal to its perpendicular supplanting ( vitamin D ) value. Knowing that a sine map Begins by swerving up from the line of symmetricalness. the horizontal stage displacement ( degree Celsius ) value can be approximated by looking at what the ten value is where the Y value is ? 18.425 and the graph is swerving up. From looking at the graph:degree Celsiuss = 12. 0Using the same premises for the maximal value. one can happen the value for a by utilizing the expression:a = 3. 225a = 3. 23Assuming that the maximal value is when Age = 20 and utilizing Age = 5 as the lower limit.

one can happen the period of the map cognizing that the difference between the x value at y soap and the ten value at y min is ? of a period. The period of the map is hence 30.One can happen the value for B utilizing the expression:

B =Using the approximated a. b. degree Celsius and vitamin D values.

The attendant equation

is: Using TI InterActive! ™ to chart that map. the attendant graph is as follows:Overlaid with the original informations. and curtailing the graph of the map to the same sphere and scope as the sphere and scope on the scatterplot. the graph of both the informations and the map together is as follows:Comparing the two graphs. one can see that where BMI = 18. 4 in the map is about 0. 400 old ages off from the corresponding point on the scatterplot where BMI = 18. 4. That can be fixed by seting the horizontal stage displacement value of degree Celsius to 12. 4 to counterbalance.

There is besides a noticeable disagreement between the map graph and the spread secret plan in the sphere and A little stretch about the Y axis would suit the curve closer to the information points in those countries. therefore the B value should be changed from ?/15 to ?/14. The figure ?/14 was chosen because cut downing the denominator’s value by 1 will increase the B value by a little sum. and an increased B value will shorten period and compact the graph about the Y axis. ensuing in the values within sphere to be closer to that of the information points. Making these alterations. the revised expression for the sinusoidal map is as follows:Using TI InterActive! ™ to chart that map. overlaid with the original informations.

and curtailing the graph of the map to the same sphere and scope as the sphere and scope on the scatterplot. the graph is as follows:The refined equation fits the informations much more closely at the beginning. yet around the Age = 13 grade

it starts to divert once more. Looking at this graph. one can come to the decision that it will take more than one mathematical map to chart the entireness of the informations.If one were to associate the construct of human growing with the mensurable value of BMI. so there is a job in presuming the graph follows a sinusoidal form when generalizing informations from the graph beyond 20 old ages of age. Based on common cognition. misss are normally finished turning at ? 20 old ages of age – yet one can see that had the sphere non been restricted in the sinusoidal map. the BMI would swerve back down and endorse up for adult females ages 20 to 38 ( the difference of 20 and 38 being ? of the period ) . Because that informations would be incorrect based on the common cognition of growing fillet after ? 20 old ages of age. one can reason that a sinusoidal map will non fit the informations in the sphere.

Using the premise that misss are normally finished turning at ? 20 old ages of age. one can believe of human growing as an case of delimited exponential growing. where a miss grows quickly as a kid before decelerating down and finally halting her growing once they have reach grownup size. With this frame of head. the mathematical map that best theoretical accounts growing towards a fixed capacity would be a Logistic Regression map.

Because a logistic arrested development map theoretical accounts informations which whose aberrance is acquiring smaller which each point. it will be best used to pattern informations from the point in which the rate

of growing is no longer turning. That can be estimated as the degree Celsius value or the horizontal stage displacement because in a regular wickedness map. 0 to is when the rate of addition starts diminishing until the soap point. degree Celsius in the revised sinusoidal map equation is 12. 4.

Therefore. the logistic map should replace the sinusoidal map in foretelling or generalizing informations in the sphere.A logistic map has the general equation of:Using the “calculate logistic function” map on TI InterActive! ™ . utilizing the information restricted to 13 to 20 old ages of age merely ( 13 is rounded up from the get downing point of 12.4 ) . one gets the undermentioned values:a = 3. 36B = 0. 208degree Celsiuss = 22. 9Using those values.

The attendant map is:Using TI InterActive! to chart that map. overlaid with the sinusoidal map in the same graph. the consequence is as follows:When the maps are allowed to generalize beyond the information points provided. one can see the great difference between the two:As expected. the sinusoidal map curves down.

increasing at the rate it is diminishing from its soap point at Age = 20. The logistic map on the other manus. does non diminish after Age = 20. Rather. it degrees off with an asymptote of 22. 9 This is much more sensible as a theoretical account of a girl’s BMI as a map of Age because of how improbable it is that one’s weight to height ratio will hold such drastic alterations every 18 old ages ( one period of the sinusoidal map graph ) .

Using the logistic arrested development map. the BMI of a 30-year-old adult

female in the US in 2000 would be 22. 7. Using the same premise that human growing is related to the mensurable value of BMI. that value is away because a human stops turning at ? 20 old ages of age and that value is more than a full unit higher than the BMI value at age 20 ( 21.65 ) based on the information. However. because BMI is non unerringly related to the construct of human growing into grownup size. and that it is instead a measuring that compares one’s tallness with one weight ; it is possible that one could maintain deriving weight to a certain point after making grownup tallness.This premise would be that one reaches grownup tallness and grownup weight at different times. doing the BMI value of tallness to stay changeless after 20 old ages of age but the value of weight to maintain on increasing until a separate tableland – grownup weight. is reached.

Therefore. the BMI value would non stay changeless after ? 20 old ages of age and it will maintain on increasing until both grownup tallness and weight is reached. Under this premise. the value found is really sensible. Besides under this premise. one can reason based on this information that the average BMI of a adult female who has reached both grownup tallness and grownup weight would be a value really near to the asymptote of the map – 22. 9.Data taken from an American beginning should non be used as a generalisation for all misss in the universe. Many external factors such as diet. wellness. quality of life and criterion of life will impact one’s

BMI.

To contrast the informations provided for American misss. the followers is a aggregation of informations from the Department of Health Statistics for the People’s Republic of China for the state of Shaanxi in 2005.Using the information from the 50th percentile ( the average value of the informations collected ) and overlaid with the graph of my sinusoidal map. logistic arrested development map and original information points. the graph is as follows:The Department of Heath Statistics have besides fitted a curve to the informations utilizing the average BMI of urban and rural misss every bit good as urban and rural male childs:One can see from this comparing that while the BMI is by and large lower across the board. the information forms for urban misss in Shaanxi and misss in the USA are highly similar.

The theoretical account of holding the information up to Age = 12. 4 plotted as a sinusoidal map and the information from 12. 4 onwards as a logistic arrested development map besides fits the information for urban misss in Shaanxi. after little alterations to values of perpendicular supplanting and horizontal stage displacement. The bulk of the people in USA live in urban conditions.so it is apprehensible that given similar life conditions the informations for urban misss in Shaanxi follows the same form. As for the BMI being lower overall. that is likely because of a lower criterion of life in Shaanxi compared USA. doing a difference in weight that is contributed to a steady diet.

Where the theoretical account fails is for the information of rural misss in Shaanxi. A sinusoidal map does non suit the information for rural misss Ages 1 –

12. 4 at all. This can be concluded from the values before and after the min point of 14. 4 BMI.

A sinusoidal map will hold symmetrical informations before and after the min point. but the informations of rural misss in Shaanxi has the informations after the min point turning exponentially while the informations before the min point decreasing in about a additive manner. Therefore. the sinusoidal theoretical account can non be adjusted to suit the information unless the sinusoidal map is abandoned wholly for additive map with a negative incline followed by an exponential growing map.

However.

the 2nd half of theoretical account. plotted utilizing a logistic map. is still likely to suit the information after some alterations to the variables. This is due to the theory behind why a logistic map is perfect in suiting informations for “growth towards a fixed capacity” .

Unless rural misss in Shaanxi ne'er reach an “adult height” or “adult weight” value. it is certain that their BMI will besides halt turning after a certain point. Had there been more informations collected by the Department for Heath Statistics – informations for adult females above the age of 18 in rural Shaanxi. this premise could be confirmed.

In decision. this survey has shown that for misss populating in urban conditions. BMI can be modeled by the sinusoidal and logistic mathematical maps. Hopefully thanks to the work done in this study. parents will be able to track whether their kids are above or below the average BMI for their age. and foretell how much their Body mass index is likely to alter in the undermentioned twelvemonth utilizing the maps derived in the study.

They will besides

be able to compare the BMI of their girls with that of kids in rural and urban China. able to judge whether their girl is over or under the average statistics. This portfolio has besides shown how the difference in life style and life conditions will alter the form of BMI as a map of Age. Hopefully this study can function as a starting point for others researching alteration in BMI over clip for people of both genders and across a much larger age span.

Reference

1. Wikipedia. the free encyclopaedia. 16 Mar. 2009. 16 Mar. 2009.
2. “Logistic arrested development. ” Wikipedia. the free encyclopaedia. 16 Mar. 2009.
3. 16 Mar. 2009. Mueller.
   William. “Logistic Functions.” Researching Precalculus.
4. 16 Mar. 2009.Shang.
5. Lei. Yong-yong Xu. Xun Jiang. and Ru-lan Hou.
6. “Body Mass Index Reference Curves for Children Aged 0-18 Old ages in Shaanxi. China. ” Department of Health Statistics 1. 1 ( 2005 ) .
7. 12 Mar. 2009df ; gt ; .“Sigmoid map. ”
8. Wikipedia. the free encyclopaedia.
9. 16 Mar. 2009. Appleby. A. .
10. Letal. R. Ranieri. G. ( 2007 ) . Pure Math 30 Workbook.
11. Calgary: Absolute Value Publications