that is a ridiculously hard SAC for only an hour.. =\
I'm not sure if I can finish it in time
The whole thing is not an hour. There was an hour for parts I and II, and then an hour for parts III, IV and V. Part V isn't part of the SAC that's posted here though. It was the toughest part and based on an assignment. I'll see if I can dig it out of the depths of my cupboard and post it.
The extra question ilovevce was talking about:
The safe medicinal use of a drug requires knowledge both of its rate of absorption by the body (which may depend on how the drug is given) and its rate of clearance (principally through the kidneys). Typically, absorption is required to be swift, whilst clearance is more gradual. A class of functions which can be used to model this process are functions of the form
. (1)
where
represents the concentration of the drug in the blood in milligrams per litre (mg/L) and
represents the time, in minutes, since administering of the drug. A, b and c are arbitrary positive constants.
a. Consider first the function where A = c = 1 and b = 2. Sketch the graph of the concentration over a suitable domain, find any stationary points, and discuss its important features. (4 marks)
b. Find
for the equation in (1) above and show that a stationary point occurs at
. (2 marks)
c. Drug concentration often has to be maintained between two values for a particular time after the drug is administered. Determine the values of A, b and c which best model; the drug concentration when both of the following conditions are satisfied:
- the drug reaches its maximum concentration of 0.5mg/L after 30 minutes
- the concentration after 2 hours is half of the maximum value. (8 marks)
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