Assignment
Drug concentration in bloodstream 1 When a patient undergoes major surgery, the anesthesiologist must make very specific mixture of drugs that will put the patient under for a specific time period. If the drugs are too weak, the patient might wake up in the middle of the procedure; if they are too powerful, there is a risk that the patient may not wake up at all. The surgery patient's health and well-being rest on the ability of the anesthesiologist to accurately and effectively administer just the right amount of medicine at the right time. How does he or she make this happen? It turns out that there is a mathematical model that describes how medicine concentration varies over time in the human body. The formula is C=At/t2+ B' where A and b are constants by various factors including the body weight of the individual, types of drugs used, and quantity of the drugs administered.
Suppose that a certain drug will only be effective if its concentration in the bloodstream is at least 4%. However, if the drug concentration exceeds 8%, then the patient may experience adverse side effects, while any amount less than 8% is safe.
1) Let t represent the number of hours since you take the medication.
2) Let values on the y-axis represent the % concentration in the bloodstream (so a y-value of 10 corresponds to 10% concentration in the bloodstream).
I. Use Desmos to plug in different values of A and B until you get a function with maximum value close to the limit to avoid adverse side effects. (Answers will vary.)
A = _______
B = _______
Rewrite the function C with your values of A and B.
II. What is the concentration of the drug after 45 minutes from taking it?
III. What happens to the concentration of the drug as t increases?
IV. How long do you have to wait for the drug to take effect?
V. Assume that a drug is out of a patient's system once the concentration has decreased to 0.7%. How long does this drug stay in someone's bloodstream?
VI. Does your model reflect a "typical" drug behavior in which a drug takes effect for about 30 minutes after taking it and lasts (i.e., has an effect) for 4-6 hours? Explain.