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

Mathematics SL

Portfolio

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:

By making the previous observation, more information can be concluded, however, in order to do so a suitable formula or function need to be found, this can be done by finding the exponential regression which is used to produce an exponential curve that best fits the given data. An exponential curve is usually shown by f(x)=abx. To find the exponential regression a graphing calculator was used and the following was found:

a≈ 10.477

b≈ 0.829

To convert this into a proper logarithmic function, the base (b) of the exponent will be converted into a base ...