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
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?
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To find the drug function m(t) for diazepam, we can use the given equation: m(t) = m(0)e^(-kt), where m(0) is the initial dosage and k is the rate constant.
1. In this case, the half-life of diazepam is 7 hours. The half-life is the time it takes for half of the initial dosage to be eliminated from the body. Since we know the half-life, we can calculate the rate constant (k) using the following formula: k = (ln(2))/half-life.
Substituting the half-life of 7 hours into the formula, we get k = (ln(2))/7.
2. Now we can find the drug function m(t) with m(0) = 5 for 0 <= t <= 48 hours. Using the formula m(t) = m(0)e^(-kt), we can substitute the values: m(t) = 5e^(-((ln(2))/7)t).
3. To graph the drug function, plot the values of t on the x-axis and calculate the corresponding values of m(t) on the y-axis. For t ranging from 0 to 48 hours, calculate m(t) using the formula in step 2 and plot the points.
4. To find how much drug remains in the blood 12 hours and 24 hours after a 5 mg dose is taken, substitute the respective values of t into the drug function and calculate m(t). For 12 hours, substitute t = 12 and for 24 hours, substitute t = 24 into the drug function obtained in step 2.
5. To determine the initial dosage of tetracycline required to have 100 mg in the blood after 18 hours, we can use the same drug function formula as m(t) = m(0)e^(-kt) and solve for m(0).
Substituting the given values, we have 100 = m(0)e^(-((ln(2))/9)(18)). Solve the equation for m(0) to find the initial dosage.
6. To approximate the half-life of a drug when the drug level in the blood decreases from 200 mg to 75 mg over a period of 12 hours, we can rearrange the drug function formula m(t) = m(0)e^(-kt) to solve for the rate constant k.
Substituting the given values, we have 75 = 200e^(-k(12)). Solve the equation for k and then calculate the half-life using the formula: half-life = (ln(2))/k.