Math Portfolio Type II

Modeling the amount of a Drug in the Bloodstream

The goal of the following investigation will be to determine the amount of a drug which is present in the human bloodstream for different durations of specified time. Foremost, appropriate variable must be established to deal with the investigation. Let “t” represent the time in hours, and let “a” represent the amount of drug in micrograms (µg). The controlled variable will be the time, because we can establish at what hour the monitoring will start and stop. The uncontrolled variable thus is the amount of drug in the bloodstream; we have no control over that and it is ultimately what we hope to discover.

Foremost, a data table is created according to the information provided in the “Amount of Drug in the Blood Stream” graph. This is done by taking all the t values and a values and organizing them into a data point chart.

Figure 1

Figure 1 shows a data point chart for the

Amount of drug vs. the time.

After the data chart table has been created, a graph to represent the information should be simple to establish using graphing software on a computer. The software chosen for this specific investigation is Graphmatica. To create this graph on the software, simply fill in the “t” values and “a” values in the data plot chart. The graph will barely be noticeable because it is positioned at the top right hand corner and continues off screen. However, to fix this problem, right click and open the Grid Range controls. Here, set the settings so that the graph goes 10 up and 10 left.

Figure 2

Figure 2 shows a graph of “Amount of Drug in a Bloodstream”. As you can see, the time intervals increase by 0.5 hours each time, while the amount of drug in the bloodstream has no pattern in its descent.

Referring to the Figure 2, the graph is an exponential regression, because it is an exponential graph which is decreasing rather than increasing. The data point graph has been established, however to find the function of this graph, a curve of best fit must be introduced. The curve of best fit basically draws a curve through the data points, trying to get as many points directly on the line to give an appropriate representation of the data. This can be done through Graphmatica as well. Simply use the graph already established, and press the “Curve Fit” button, which draws the curve of best fit automatically. The curve of best fit essentially is the graph in a linear graph, thus to find the function of the graph, all we have to do is find the function of the curve of best fit. In Graphmatica, drag the curser to the curve of best fit. At the bottom of the screen, the program automatically gives you the function associated with the curve. The function is there fore:

a= 0.00031t4 + 0.005t3 + 0.0325t2 – 1.33t + 9.6

Figure3

Figure 3 shows the curve of best fit. The curve of best represents the function, thus the function is: a= 0.00031t4 + 0.005t3 + 0.0325t2 – 1.33t + 9.6

The graph created compared to the graph given is subsequently steeper. This has to do with the window settings. Where the given graph is forced to confine into a smaller space, this graph is able to expand and have a larger scale, showing how it truly looks.

The second problem faced within this investigation instructs the patient to take 10 µg ...