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?
To answer these questions, we need to understand the equations and concepts given in the problem. Let's break down each question and explain how to find the answers:
1. To find the rate constant k for ibuprofen with a half-life of 1.5 hours, we can use the formula:
k = ln(2) / t1/2
Substituting the given half-life of 1.5 hours, we have:
k = ln(2) / 1.5
Solving this equation, we find the value of k.
The function that gives the drug level after t hours is given by:
m(t) = m(0) * e^(-k*t), where m(0) is the initial drug amount.
To graph the drug function with m(0) = 400 for 0 ≤ t ≤ 10 hours, we can plot points by substituting different values of t into the function.
To find how much drug remains in the blood 4 hours and 8 hours after a 400-mg dose is taken, we calculate m(4) and m(8) by substituting t = 4 and t = 8 into the drug function.
2. To show that if the half-life t1/2 of a drug is known, then its rate constant k = ln(2) / t1/2:
We already know that the formula for k is k = ln(2) / t1/2. You can use this formula to find the rate constant for any drug with a known half-life.
3. To determine how many hours after taking a dose of ibuprofen the amount of drug in the blood reaches 1% of the initial dose:
We need to find the value of t when m(t) = 0.01 * m(0) in the drug function. Substitute these values into the equation and solve for t.
4. To find the drug function m for diazepam, which has a half-life of 7 hours:
Use the same formula as before, m(t) = m(0) * e^(-k*t), but now with the given half-life of 7 hours. Find the rate constant k using k = ln(2) / t1/2, and substitute it into the equation along with the initial drug amount m(0).
To graph the drug function with m(0) = 5 for 0 ≤ t ≤ 48 hours, plot points by substituting different values of t into the function.
To find how much drug remains in the blood 12 hours and 24 hours after a 5-mg dose is taken, calculate m(12) and m(24) by substituting t = 12 and t = 24 into the drug function.
5. To determine the initial dose of tetracycline needed to have 100 mg in the blood 18 hours after an injection:
Use the formula m(t) = m(0) * e^(-k*t) with the given half-life of 9 hours. Substitute the values of t and m(t), and solve for m(0).
6. To find the approximate half-life of the drug given the information that the drug level in the blood is 75 mg 12 hours after a 200 mg dose:
We need to find the value of t when m(t) = 75 and m(0) = 200 in the drug function. Substitute these values into the equation and solve for t.
Remember to use the formulas and concepts explained above to solve each question step by step.