Injection Suppose m_ 0_ milligrams of a drug are put in the blood by an injectio
ID: 2832227 • Letter: I
Question
Injection
Suppose m_0_ milligrams of a drug are put in the blood by an injection. The amount of drug t hours after the injection is given by
m(t) = m_0_e^(-kt), for t >= 0
Where k is the rate constant, which is related to the half-life.
4. The sedative diazepam has a half-life of 7hr. Find the drug function m for diazepam. Graph the drug function with m_0_=5 for 0<= t<=48 hours. How much drug remains in the blood 12hr and 24 hr after a 5-mg dose is taken?
5. The antibiotic tetracycline has a half-life of 9 hours. Suppose a doctor wishes a patient to have 100 mg of tetracycline in the blood 18 hours after an injection. What initial dose meets this requirment?
6. Twelve hours after a 200-mg dose of a drug is injected, the drug level in the blood is 75 mg. What is the (Approximate) half-life of the drug?
Explanation / Answer
i have done 4th in the other question post ...
will do 5 and 6 here
5)
half life = 0.693 / K
K = 0.693 / 9 =0.077 per hour
m(t) = m_0_e^(-0.099t) -------------------- drug function
given m(t) = 100 ; t=18 hours
100 = m_0_ e^(-0.077*18)
m_0 = 399.8823 mg
6)
m(t) = m_0_e^(-kt)
after t=12 hours
m_0 = 200 mg
m(12) =75
put these in the equation
75 = 200 * e^(-K *12)
0.375= e^(-K *12)
apply ln on both sides
ln(0.375) = ln[ e^(-K *12)]
-0.981 = -12K
K = 0.081736 per hour
half life = 0.693 / K
= 0.693 / 0.081736
= 8.479 hours
K=