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Calculus/Physics Please help!!

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An intravenous line provides a continuous flow of drug directly into the blood. Assuming no initial drug in the blood, the amount of drug in the blood t hours after the dosing begins
in m(t) - (a/k)(1-e^-kt), for t (=>)0, where k is the rate constant (again related to half life) and A is the rate at which drug flows into the blood (in units of mg/hr)

Suppose an antibiotic with a half life of 12 hours is given to a patient intravenously at a rate of A=50mg/hr.
find the rate constant k
what is the steady-state level of the antibiotic in step 7? that is, evaluate lim(t-> infinity)m(t).
In general, what is the steady state level of a drug delivered by infusion in terms of A and K?
in general at what time does the drug level reach 90% of the steady state level, in terms of A and K?
Based on patients weight, a doctor targets a steady state level of tetracycline of 100mg through infusion.
what infusion rate A should be used? The half life of tetracycline is 9 hr.
in step 10, at what time does the drug level reach 90% of the steady state level? At that time,
how much drug has actually been delivered?
Suppose a patient has been on infusion of tetracycline for 72 hours with infusion rate as found in step 10,
when the delivery is terminated. How long does it take for the drug level in the blood to reach 2mg?

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