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Modelling the Amount of a Drug in the Bloodstream - Lab Report Example

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This paper "Modelling the Amount of a Drug in the Bloodstream" discusses the amount of drug in the bloodstream based on the data given for a drug for treating malaria in the bloodstream over the 10-hour period following an initial dose of 10 μg…
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Modelling the Amount of a Drug in the Bloodstream
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Download file to see previous pages At last, cases will be taken for the patient, for no further doses taken and doses continued to be taken for every six-hours for a period of one week.

As given, from figure 1, it is clear that the rate of the decrease of the drug is approximately proportional to the amount remaining. In addition, the graph is similar to an exponential decay graph because the amount is subject to exponential decay as it decreases at a rate proportional to its value. Therefore, for modeling, the exponential decay function will be used. The general equation of an exponential decay function is written as below:
Where, is an initial value at t = 0, is decay constant, is the time and is the amount remaining after time. Like (pie), it is also an irrational number, which is used in natural logarithmic (ln) and the value of is approximately 2.7182818284590452353602874713527.
Let us use the natural exponential decay function, for modeling the amount of drug in the bloodstream. At the start, the drug given to malaria patients is 10 µg. Therefore, the value of will be 10. For simplicity let us use instead of. Now, the equation can be written as:
The data given is not precise, therefore, for each interval (hours) the value of (decay constant) will be different. For calculating the approximate value, the value of each data will be calculated and their average will be taken. Simplifying function, for calculation of decay constant.
There are 20 records for the amount of drug remained, therefore, the value of decay constant calculated for each record will be different. The above-derived function can be used for calculating different values for the given data.
Figure 2 shows the Graph of model function and the data given for the amount of drug in the bloodstream over a period of 10 hours. Now, from figure 2, it can be seen that both graphs of model function and graph of data give follows the approximately the same path. There is a minor difference in-between periods 2-3 and 5-6 hours. However, for the rest of the points (period), model graph function follows the same path as a graph of data given. ...Download file to see next pagesRead More
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