a. After a dose, the concentration of medication in the blood declines due to metabolic processes. The half-life of a medication is the time required after an initial dosage for the concentration to be reduced by one-half. A common model for this process is
C(t) = C(0)e-kt
where C(0) is the initial concentration, t is time (in hours), and k is called the elimination rate constant, which varies among individuals.
For a particular bronchodilator, k has been estimated to be in the range 0.047 ≤ k ≤ 0.107 per hour. Find an expression for the half-life in terms of k, and obtain a plot of the half-life versus k for the indicated range.
b. If the concentration is initially zero and a constant delivery rate is started and maintained, the concentration as a function of time is described by
where a is a constant that depends on the delivery rate. Plot the concentration after 1 hr, C (1), versus k for the case where a = 1 and k is in the range 0.047 ≤ k ≤ 0.107 per hour.
