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suppose m(0) milligrams of a drug are put in the blood of an injection. The amount of drug t hours after the injection is given by
m(t)=m(o)e^-kt, for t (=>) 0, where k is the rate constant, which is related to the half life. we also treat oral administration
of drugs as an injection, although the model is less accurate because of the drug must be absorbed into the blood through the stomach

1.
ibuprofen has a short half-life of 1.5 hours. find the rate constant k for ibuprofen and write the function that gives the drug level after t hours.
graph the drug function m with m0=400 for 0(<=)t(<=)10 hours. how much drug remains in the blood 4 hr and 8hr after a 400-mg dose is taken?

2.
show that if the half-life t1/2 of a drug is known, then its rate constant at k=ln 2/t 1/2
3.
how many hours after taking a dose of ibuprofen does the amount of drug in the
blood reach 1% of the amount of the initial dose?
4.
the sedative diazepam has a half-life of 7 hr. 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 12 hr 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 a 100mg of tetracycline in the blood 18 hours after an injection. what initial does meets his requirement?
6.
twelvee hours after a 200 mg dose of a drug is injected. the drug level in thebloodd is 75mg. what is the approximate half-life drug?

1.
.5 = e^1.5k
ln .5 = 1.5 k
ln.5÷1.5 = k
m(4) = 400e^4(ln.5÷1.5)=62.996 mg
m(8) = 400e^8(ln.5÷1.5)=9.921 mg
2.
If half life =t1/2
.5 = e^kt1/2
ln.5 = kt1/2
k=ln.5/t1/2 hr
3.
.01 = e^t(ln.5÷1.5)
ln.01 =t( ln.5 ÷1.5)
ln .01/( ln.5 ÷1.5)=t
9.966 hr=t