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

Mathematics SL Portfolio Type II Modeling the amount of drug in a bloodstream

Extracts from this document...


Mathematics SL


 Type II

Modeling the amount of drug in a bloodstream

                                                                                                                             November 30, 2007

The use of math in life is extremely beneficial; one can know or at least predict what to expect, why to expect it and how to find it. An example of an application of math in life would be medicine; doctors can calculate how much medicine to prescribe and how long it lasts or how long it takes for it to decay, therefore, how often should the patient take it.

In a case for treating Malaria, an initial does of 10 milligrams (μg) of a drug was given and an observation for a total period of 10 hours was done, the amount of drug was measured every half an hour, the results were plotted on the following graph(figure 1):



As can be seen, this graph shows the rate of the breakdown of the drug in the blood where the amount of drug in the bloodstream decreases with time; they are inversely proportional. In the following table are the numerical results of this observation taken from the previous graph:  

Time in hours


Amount of drugs in μg










Time in hours


Amount of drug in μg


































...read more.


ec = b1

ec ≈ (0.829)1

c = ln(0.829)

c ≈ -0.2

Therefore, b ≈ e-0.2

And so, f(t) = 10.477e-0.2t where (t) is the time taken for the amount of drug to change in the bloodstream.

The function previously found will help in making a model to predict the change in the amount of drug in the bloodstream over long periods of time without having to expose the patients directly to the drug just in case something might go wrong. The following graph (figure 2) shows the difference between the function for the model and the data plotted in (figure 1) along with its curve-fit to raise the aware of the fact that a model does not 100% apply in real life.



As shown in (figure 2), the function is accurate enough to be used in making predictions as the curve is close enough to the plotted points and it also crosses the curve-fit at some points as well.

...read more.



It can be seen that the drug will completely breakdown after less than 3 days. However, according to the model in (figure 5) below, if the patient continued to take the drug every six hours for a week, the amount of drug will always reach the same maximum amount of 15.0μg and a minimum amount of 4.5μg after a period of 60 hours, this concludes that the rate of decrease of the drug is almost proportional to the amount remaining.



Using a math application in such a case is greatly useful and helpful in order not to make errors in real life for if a patient, such as in the previous case, was given a wrong does of medication it might cost them their life. This indicates that there are always practical uses for mathematics in life as well as protective ones.

...read more.

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

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    �{��gK -�-�i$�q�_ ßE�O�� �H��bX'������"�Q(r)5j"�1/2n�:���1O�~�i���(nl�5�"�K�$�%�>:w�l�s8\gx�e�L���@�.Ù·o��۷�=ztÛ¶m�d`@w�y' �(�(c)�0�@ *�*"$3/4<j8�?�G�u� Eb�C%[dj��YZ1/4x1��v����*3/4�-h�E���>b�c�Lmz5 "i'��^�q"�$9[�"�Q.<��ΥE)Re,R#Gx�é§N��;�1/4dh��� [qÇ7�x�yt��{��Ͳ1/2C0ТE����=�'�1/27n+�>}�=���L �$�c��...�< �A#��-��Í7�E��\"3/4��I[��0×���6����inB�� \<[�3���]�-%I��ٳ':EÒ (r)CL<�B_m�ZW5d�1/4o�E<-Y��Ν;�m�f���J���R��>�D�%�" �...�bz�\c�`2x/(c)��+����'��...0��-(1I�%�(Î9rΜ9]7n-J�5��% �0�d ���պR�<1 Q �w��]Tl��H�DM�8\j]ÖÚ� a]1��`'$(r)>��"),���-z�m�RX�"C��G�Y��1J�ҪU""�3/4"�(tm)Sxj�e8 ?���<��s�`r-�w�d]�HcRb\-� ����a�(r)8�c��|Q.�Zw�s��W\���gN1�o~�|A�$�7p��Æ9���� .��"if'���!2G:?��#D�4(^F'2���U�è¢ï¿½G�,��!�$���Up'o3/4�& 0-'���� 7v�)�\�vĪ�ִ�gkΜ n��S>��Ø���^��_��,á¡-Â��r^{�5*�P�0yJx��"-?�e...�ӹ(_WM �1�"̱�v*t�/��"(n�1/2{��~�m�"�;�-��%q6�'-9���%...t�B�X���"�M�R��"�Y�?�|3%jM'~��b �/�� t�A0M�#�H�p%�b51���bqqIrW�2M,X��o���� ��...i(tm)J(r)_��W%�Î$~S �)3/4`3/4)O ���Y�t�)���PY� ��&|�"p'�I=��<ꨣL�12�$ï¿½ï¿½Ï ï¿½1o���b"��_~?�;�~(n�y� ��~�9��*x9����?�$F�$B(r)�26l���O)b��((tm)�Y|Ô¨Q�G~�"����I�h1/4L�� 0��N#��q��t��1/4g�-� f�E� �&���kÒ¤I�>��a�V��-�a�֭�E BA?�'2�|�h���(tm)9�'�x���1/2�c�A �PiÖY�kb-LfΜi�B-1/4��s:1/2-T�S��g#�nM �1v ��O�]| �" |��g �xg� �O�'- ����7o-�,l�H3/4��"���g7'S[x���"��v$�`1/4+ :��"�6a^��3/4��FoN���Qd""3z� �q�֭c9&�"�Ce�m f �+�����l@_s����ܹs��{�C���"\q "obl�0a��� �m�С� r�s\�{�-M�1v�� ���O�|\����(r)K�U+�-��l 'S[�r �"�+xÜ|�l'�'�#������t��aO+_ �k�6�x�$'�(c)mzK����BÙ��ۿ5�dE��qÚr PNÈ£e��v\U�2�.

  2. Tide Modeling

    It is also important to notice that they need to be in the same position of the period. For reference it was measure the top two points of the crests, and the two low points of the trough. Once the two points are measure it is necessary to find the difference between the two points.

  1. IB Mathematics Portfolio - Modeling the amount of a drug in the bloodstream

    The only difference is the original data didn't have the line of best fit on it. It still contains the same data points and scale. The r2 or the coefficient of determination displays how closely my model fits the data.

  2. Math Portfolio: trigonometry investigation (circle trig)

    are formed to see any constraints on the values of b. The maxima of the graph is 1 and the minima of the graph is -1. The amplitude in the graph is calculated by, resulting to 1. The period in the graph is which approximately 18.8496 when expressed to radian are.

  1. Modelling the amount of a drug in the bloodstre

    o Fits the model equation y=ax+b to the data using a least square fit. It displays values for a ( y-intercept) and b (slope) * Quadratic regression (ax�+bx+c) o Fits the second degree polynomial y=ax�+bx+c to the data. It displays values for a,b, and c.

  2. Mathematics (EE): Alhazen's Problem

    Relating back to our focus question - if we had two balls in a circular billiard table, and we were able to relate their positions into (x,y) coordinates on a plane and also measure the radius of the table, then we would be able to find the exact point(s)

  1. Type II Portfolio - BMI

    The BMI is calculated by taking one's weight in kilograms and dividing it by the square of one's height in meters. After about the age of 20, the growth in height of women generally stops. If this is the case, the denominator in the calculation would generally stay the same.

  2. Mathematics internal assessment type II- Fish production

    Therefore, a new model must be suggested for this set of data points. Suggesting new model for Fish Farm Just as the previous graph, this graph can be described by a piecewise function, and hence this graph will also be broken into 3 intervals namely, 2004?x?2006 2001?x?2003 1980?x?2000 Graph for

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work