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

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Introduction

MINZY NGUYEN IB SL I 4/19/07 Modeling the amount of a drug in the bloodstream Description of task The graph below records the amt of a drug for treating malaria in the bloodstream over 10 hrs following an initial dose of 10 micrograms. Student must find a suitable function to model the data given and compare and analyze the student's model to the given data. Finally, interpret the data by stating limitation and modification for the model and how the model can be applied to real life situations. Original Data Given: Part A Find a suitable function for your graph and comment on it. MODEL A MODEL A A1. This model demonstrates the exponential decay relationship between the time in hours and the amount of drug left in the bloodstream. According to the model data, the amount of hours increases as the amount of drug in the blood stream decrease. The function of the trend line is y= 10.391e^-1863x. The coefficient of determination is .9942. "The rate of decrease of the drug is approximately proportional to the amount remaining." A2. Method First, I start by making a scatter plot using the Excel Program. I enter the x and y values (data) given on the task sheet into two columns. Then I add the exponential trend line for the line of best fit by right clicking the data points on the scatter plot and "add trend line". ...read more.

Middle

After 12 hours there will be 4.3 micrograms left in the bloodstream, and it goes on building up higher. Another reason I assume that is because some medication labels would something like "take this drug for 5 days and if the illness continues, stop taking this drug and see your doctor." I predict that the manufacturer of the drug do not want the person taking the drug to have excess amount of the drug inside his/ her bloodstream because the patient is continuously taking it. 2. Data points for model B (model B on next page) 0 10 12.5 13.192 0.5 9 13 12.01867 1 8.3 13.5 10.9497 1.5 7.8 14 9.9758 2 7.2 14.5 9.0885 2.5 6.7 15 8.2802 3 6 15.5 7.54369 3.5 5.3 16 6.8731 4 5 16.5 6.26145 4.5 4.6 17 5.7046 5 4.4 17.5 5.19716 5.5 4 18 14.7349 6 13.7 18.5 13.42432 6.5 12.48141 19 12.23 7 11.391 19.5 11.1425 7.5 10.35988 20 10.15 8 9.4384 20.5 9.2486 8.5 8.599 21 8.42597 9 7.8341 21.5 7.6765 9.5 7.1373 22 6.9938 10 6.5025 22.5 6.3717 10.5 5.92417 23 5.805 11 5.3923 23.5 5.2887 11.5 4.9172 24 4.818286 12 14.4799 Model B This graph models the amount of drug in bloodstream over a 24hr period of time. On the graph, I can see that the dose is added every six hours and the slope gets slightly steeper every time because of the increasing gap between the first two dots after each new dose. ...read more.

Conclusion

Everyone's biological processes in the body are different. Every drug will not have the same effect in everyone. Some, the drug might help them recover fully from this malaria after taking the drug for a week while some people have to continuously taking the drug for months to get the same results. What if the person was taking another drug along with this current drug? I think that if another drug is taken while this drug is also taken, one drug might cause the other drug to decay faster in the body. The model can not accurately represent what will happen because often, people take drugs without first asking a doctor. A common person would not know what would happen if two different drugs were taken together. There are too many different factors that needed to be controlled for the model to work, so I do not think this is a very accurate model. Maybe the model is accurate to a certain extent. It should only be an approximate model of amount of drug in the bloodstream. Currently, I can not think of anything to modify this model to make it more accurate. ?? ?? ?? ?? This document was downloaded from Coursework.Info - The UK's Coursework Database - http://www.coursework.info/ This document was downloaded from Coursework.Info - The UK's Coursework Database - http://www.coursework.info/ This document was downloaded from Coursework.Info - The UK's Coursework Database - http://www.coursework.info/ This document was downloaded from Coursework.Info - The UK's Coursework Database - http://www.coursework.info/ ...read more.

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