calculus

posted by .

Hydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity of drug in the body decreases at a rate proportional to the amount left in the body, with constant of proportionality . Suppose that the half-life of hydrocodone bitartrate in the body is 3.7 hours, and that the oral dose taken is 12 mg.

(a) Write a differential equation for the quantity, , of hydrocodone bitartrate in the body at time , in hours, since the drug was fully absorbed.

  • calculus -

    amount = 12 (1/2)^(t/3.7) where t is in hours.

  • calculus -

    However, to answer the question,

    da/dt = ka

    The boundary conditions will reveal that
    k = ln(1/2)/3.7

  • calculus -

    Oops forgot about the 15. Toss it in as needed.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A patient is given a drug intravenously at a rate of 43.2 mg/hour. The drug enters a compartment volume or the volume of the part of the body of 35,000 ml. The rate at which the drug leaves the body (mg/hour) is proportional to the …
  2. Pre Calc!

    A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t)=10(0.8)^t and that in order for the drug to be effective, at least 2 milligrams …
  3. Pre Calc!

    A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t)=10(0.8)^t and that in order for the drug to be effective, at least 2 milligrams …
  4. PRE-CALC

    A drug is eliminated from the body through urine. Suppose that for an initial dose of 10 milligrams, the amount A (t) in the body t hours later is given by A(t) = 10(0.8) t a) Estimate the amount of the drug in the body 8 hours after …
  5. calculas

    Hydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity of drug in the body decreases at a rate proportional to the amount left in the body, with constant of proportionality . Suppose that …
  6. Pre Calculus

    When doctors prescribe medicine at equally spaced time intervals, they are aware that the body metabolizes the drug gradually. After some period of time, only a certain percent of the original amount remains. After each dose, the amount …
  7. Pre-Calculus

    At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount A, in mg, remaining in the body is given by A=13(0.82)^t. a) What was the initial amount taken?
  8. Calculus (math)

    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 …
  9. Calculus II Help Please

    Only question I can't do on the assignment In pharmacokinetics the area under the graph of the drug concentration function with respect to time can be used to determine the total amount of the drug absorbed (the area is actually proportional …
  10. Math

    the amount (in milligrams) of a drug in the body t hours after taking a pill is given by A(t)=30(0.8)t . (a) What is the initial dose given?

More Similar Questions