Question

A certain drug has a half-life in the bloodstream of 2 hours. Doses of D mg will be administered every 6 hours, with D to be determined. a) What percentage of a single dosage remains after 6 hours?; after 12 hours?

b) Express the number of milligrams of drug in the bloodstream after the nth dose has been administered as a geometric series.

c) What is the long-run level of the drug in the bloodstream, assuming that D mg continue to be administered every six hours?

d) If more than 400 mg of drug in the bloodstream is considered to be a dangerous level, find the largest possible dose that can be given repeatedly (every six hours) over a long period of time.

e) For each dose of D mg, the amount remaining in the bloodstream after t minutes is given by De^-ct for a positive constant c.

i) Suppose D mg are administered every T minutes (instead of every six hours). How much of a single dosage remains after T minutes?; after 2T minutes?; after 3T minutes?

ii) Express the amount of drug in the bloodstream after the nth dose has been administered as a geometric series.

iii) What is the long-run level of the drug in the bloodstream, assuming that D mg continue to be administered every T minutes?

iv) Assuming a half-life of 2 hours (120 minutes), find the value of the constant c.

v) If the dose D is 100 mg, and more than 400 mg of drug in the bloodstream is considered a dangerous level, how frequently can the drug be safely administered?

Answer 1