Ibuprofen And Acetaminophen

Math Internal Assessment
Investigating the effectiveness of the drugs Ibuprofen and Acetaminophen
Personal Code: gkw125

Mathematics SL Internal Assessment
Background:

Whenever we are in pain, let it be headaches or even back pain, the first source of remedy that we always seek is from over the counter painkillers such as Aleve and Advil. One of the problems or even a dilemma that we face between buying a painkiller is determining which painkiller would prove to be the most effective in remedying the pain and providing quick relief. When taking pain killers we also have to consider how quickly and how much should be absorbed in the blood to provide the maximum benefit. Some drugs need to be absorbed quickly in the blood
Although the same dosage of 200 mg was used for both ibuprofen and Acetaminophen, when comparing the AUC values and the Cmaxvalues it can be determined that Ibuprofen is more effective in providing quick pain relief when compared to Acetaminophen. Since we now have the AUC values, the rate of absorption and the rate of elimination of Ibuprofen and Acetaminophen can be determined through
When the AUC was calculated, the area of each segment within certain time intervals were added up, For each of these individual segments the approximate area was calculated by finding the plasma concentration equation and integrating through definite integration. Finding the total AUC could be represented by the equation below:
AUC= t= 0t= Cptdt
Where Cptrepresents the Plasma concentration equation of each individual segment.
When observing the general shape of any pharmacokinetic profile, it is evident that they all follow the shape and curve of an exponential function.This allows us to express Cptas:
Cpt= Cp0e-kelt= DoseVe-kelt
We can now substitute this equation into the previous equation to create an analytical equation for determining AUC.
AUC= t= 0t= DoseVe-keltdt t= t1t= t2e-keltdt=e-kt-kt= t1t= t2= e-kelt2-k-