Homework SourseBackground A dosage of a certain drug is administered to an
Background: A dosage of a certain drug is administered to an individual. Assume that the drug is administered intravenously, so that the concentration of the drug in the bloodstream jumps almost immediately to its highest level. The concentration of the drug then decays exponentially.
Specifics: A doctor prescribes a 240 milligram (mg), pain-reducing drug to a patient who has chronic pain. The medical instruction reads that this drug should be taken every 4 hours. After 4 hours, 60% of the original dose leaves the body.
1. Supposing that the patient takes just one dose of the medicine, write an equation for the amount of the drug in the patient
Specifics: A doctor prescribes a 240 milligram (mg), pain-reducing drug to a patient who has chronic pain. The medical instruction reads that this drug should be taken every 4 hours. After 4 hours, 60% of the original dose leaves the body.
1. Supposing that the patient takes just one dose of the medicine, write an equation for the amount of the drug in the patient
Solution
This process can be modeled by the equation concentration of drug at time \'t\' is given by C(t) = C.exp(-kt) mg we have two conditions at t = 0, C(t) = 240mg put this in equation to get constant, C = 240 next after 4 hours, 60% of drug has left the body. So remaining 40% is there. hence at t=4 drug present is 96mg put this in eqn we get, 96 = 240exp(-4k) hence k = 0.2291 So the equation becomes C(t) = 240exp(-0.2291t) ...[C in milligrams and t in hours] just after second dose, Concentration, C = 240 + 240exp(-4*0.2291) = 336mg
