Blood Stream Concentration Lab Report
In this folio task, the impact of drug absorption and blood stream concentration, on the human body, will be observed. The rate of absorption and clearance of the drug, relies on many factors. The drugs blood stream concentration, time of administration, absorption rate, clearance rate and the effect of certain parameters, will be calculated.
This can be completed through using a surge function, calculus (derivatives) and straight line graphs (). Graphing technology on the graphics calculator and Desmos will be incorporated, to assist calculations. Additionally, Laxatives will be researched, and a mathematical model will be made to represent its individual characteristics.
An equation can be constructed to model the concentration …show more content…
The constants and , will vary depending on the type of drug and person. Figure 1 is the graph produced by the equation, . This will result in a surge function (see Figure 1).
The independent variable is the time () in hours, after the drug was given. The dependent variable is the concentration () of the drug in the blood stream (), which is measured in milligrams per litre. This is because, ‘’ determines what the value of is. A reasonable domain for this graph is . Once the drug is consumed, the time is 0. Hence, why it is impossible to have a concentration in negative time. Additionally, after the 14th hour the concentration level is too small to be considered. Similarly, the range is , since the concentration starts at 0 and the maximum is less than 4mg/L.
Figure 1 shows that the concentration was 0.372mg/L after one hour, 3mg/L after three hours and 0.0081mg/L after fifteen. It takes the drug 37.8 minutes to reach a concentration of 0.1mg/L, and then 11 hours and 27 minutes to drop back down 0.1mg/L. The person had a total of 10 hours and 49 minutes with a blood concentration above 0.1mg/L. The maximum concentration of the drug was 3.2mg/L, which occurred after approximately 3 hours and 40 minutes. The first hour had an average absorption rate of
This can be completed through using a surge function, calculus (derivatives) and straight line graphs (). Graphing technology on the graphics calculator and Desmos will be incorporated, to assist calculations. Additionally, Laxatives will be researched, and a mathematical model will be made to represent its individual characteristics.
An equation can be constructed to model the concentration …show more content…
The constants and , will vary depending on the type of drug and person. Figure 1 is the graph produced by the equation, . This will result in a surge function (see Figure 1).
The independent variable is the time () in hours, after the drug was given. The dependent variable is the concentration () of the drug in the blood stream (), which is measured in milligrams per litre. This is because, ‘’ determines what the value of is. A reasonable domain for this graph is . Once the drug is consumed, the time is 0. Hence, why it is impossible to have a concentration in negative time. Additionally, after the 14th hour the concentration level is too small to be considered. Similarly, the range is , since the concentration starts at 0 and the maximum is less than 4mg/L.
Figure 1 shows that the concentration was 0.372mg/L after one hour, 3mg/L after three hours and 0.0081mg/L after fifteen. It takes the drug 37.8 minutes to reach a concentration of 0.1mg/L, and then 11 hours and 27 minutes to drop back down 0.1mg/L. The person had a total of 10 hours and 49 minutes with a blood concentration above 0.1mg/L. The maximum concentration of the drug was 3.2mg/L, which occurred after approximately 3 hours and 40 minutes. The first hour had an average absorption rate of