Suppose Ct is the concentration of a drug in the bloodstream at time t, A is the

Question

Suppose Ct is the concentration of a drug in the bloodstream at time t, A is the concentration of the drug that is administered at each time step, and k is the fraction of the drug metabolized in a time step.

(a) What is the recursion that models the dynamics of drug concentration?

Ct+1= ?

Suppose Ct is the concentration of a drug in the bloodstream at time t, A is the concentration of the drug that is administered at each time step, and k is the fraction of the drug metabolized in a time step. (a) What is the recursion that models the dynamics of drug concentration?

Explanation / Answer

C?t?+1= C?t+A- (C?t+A)K = (C?t+A)(1-K)

since concentration after a unit of time = concentration at time t + A which is the concentration of drug given

but since a part of this would get metabolised, the amount metabolised would be = (C?t+A)K

Amount left out would be: C?t+A- (C?t+A)K

thus concentration at time t+1 = C?t+A- (C?t+A)K = (C?t+A)(1-K)

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