A medicinal pill, e.g., decongestant or antihistamine, is swallowed by a patient and enters the Gastro-Intestinal Tract (GI-Tract), whereupon it dissolves and then diffuses into the Bloodstream. Finally, the medicine leaves the body through Kidney and Liver removal.
We consider two instances:
(a) Just one pill with $P$ mg of the medicine is administered.
(b) A regimen of pills, one per hour, each with $P$ mg of the medicine is administered.
- For both (a) and (b) model the amount of medicine in both the GI-tract and the Bloodstream over time in hours. Be sure to make your assumptions clear and relevant.
- In both cases, describe the amount of medicine in each compartment (GI-Tract and Bloodstream) with a plot based one some numbers you think are reasonable from your understanding of taking medicine, e.g., a doctor says, ``Take one every four hours.''
- Describe the long term behavior of the amount of medicine in each compartment (GI-Tract and Bloodstream).
- Reflect on the reasonableness of your model results.