Warfarin is a drug used as an anticoagulant. After administration of the drug is
ID: 3028352 • Letter: W
Question
Warfarin is a drug used as an anticoagulant. After administration of the drug is stopped, the quantity remaining in a patient's body decreases at a rate proportional to the quantity remaining. Suppose that the half-life of warfarin in the body is 39 hours. Sketch the quantity, Q, of warfarin in a patient's body as a function of the time, t (in hours), since stopping administration of the drug. Mark 39 hours on your graph.
A) Write a differential equation satisfied by Q: {dQover dt} = (Your equation should not involve any undetermined constants.)
B) How many Hours does it take for the drug level in the body to be reduced to 30 percent of its original level? time =
Explanation / Answer
A) given that
dQ/dt =-QK
where k is proportanility conatant
dQ=-Qk dt
dQ/Q=-k dt
intigating on both side
ln Q = -kt +c
at t=0 Q=Q0
c=ln Q0
therefore ln (Q/Q0) =-kt
at t= 39
Q/Q0= 0.5
ln 0.5 = - k.39 k=0.01777
ln (Q/Q0) =-0.01777t
B)
when Q/Q0=0.3
ln 0.3 = -0.0177t t = 67.74 h