a.) After a dose, the concentration of medication in the blood declines due to m

Question

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 to 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

C(t)=(a/k)(1-e^(-kt))

where a is a constant that depends on the delivery rate. Plot the concentration after 1hr, c(1), versus k for the case where a=1 and k is in the range .047<=k<=.107 per hour


Please put the command for matlab to solve this problem and explain step by step what you are doing

Explanation / Answer

the amount of lead 210 in a sample t years after it was mined is the solution of the differential equation dy/dt = -ky +r k = to the decay constant for lead 210 r = the rate at which the small amount of radium 226 in the sample decays into lead 210 (treat as a constant) lead 210's half life = 22 years

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