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Modelling the Amount of a Drug in the Bloodstream - Assignment Example

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"Modelling the Amount of a Drug in the Bloodstream" paper models the amount of drug (μg) for the treatment of malaria in the bloodstream. The model function that represents the amount of drug over the period is derived and the suitability of this model function is discussed. …
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Modelling the Amount of a Drug in the Bloodstream
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Download file to see previous pages The amount of drug (μg) for treatment of malaria in the bloodstream after an interval of 0.5 hours (30 minutes) for 10 hours is recorded in the given graph as shown in figure 1. From this graph, the values of the amount of drug (μg) after 0.5 hours are taken and presented in table 1. Below figure 2 is plotted based on table 1 data.

However, it is easier for modeling when we take the value of ‘n’ as ‘e’1 because for simplifying exponential equation it is easier to take the value of ‘n’ as ‘e’. this type of exponential equation is called as “natural exponential equation”2 and can be written as :

The above equation is a natural exponential equation of growth, i.e. the value of will increases as the value of x increases. If we replace ‘c’ to ‘-c’, then this equation will become a natural exponential equation of decay.

Now, from figure 2 graph it is obvious that the amount of drug decreases with time, therefore it is of type of an exponential decay graph. A natural exponential decay function can be represented by:3

From the above figure 3, it is seen that the graph of model function follows a similar decrease (decay) as the data given for the amount of drug remained over a period of time. Therefore, the model function represents the type of decay that is given in a graph of figure 1.

The patient is instructed to take 10 µg of a drug every six-hour. From a given graph (figure 1 and table 1), it is seen that the amount of drug remained after six hours is 3.7 µg. Let assume that this is the amount of decrease for every six-hour period. Therefore, when the second dose is given to the patient than the initial amount will be 13.7 µg at the start of the 7th hour. Similarly, at the start of the 13th, and 19th hour the initial amount will be 17.4 µg and 21.1 µg respectively. This is presented in below table 3.

The patient is instructed to take 10 µg of the drug every six-hour.  ...Download file to see next pagesRead More
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