The Problem: Drugs in Series. Questions are provided in the following pictures.

The Problem: Drugs in Series1 One of the physician's responsibilities is to give medicine dosage for a patient in an effective manner. Two mathematical techniques help physicians analyze the concentration of drug is the bloodstream of a patient: the exponential decay model (EDM) and the Geometric Series and its Formula (GSF). In this problem, we will analyze the situation where a drug is administered intravenously and that the concentration of the drug in the bloodstream jumps almost immediately to its highest level after a dose is administered. Let Q(t) be the dose concentration of a drug at time t, and Q0 represent the concentration just after the dose is administered intravenously. a) According to the EDM, as the body eliminates the drug, the rate of decrease of concentration in the blood is proportional to the concentration itself. If Q0 represents the concentration just after the dose is administered intravenously, explain why the amount of drug after t hours is given by Q\") = 6206,\" where k is a constant (depending on a property of the particular drug used). b) Now suppose that at t = c, a second dose of the drug is given to the patient. The concentration of the drug in the bloodstream jumps almost immediately to its highest level (2(0) and then the concentration is diffused rapidly throughout the bloodstream over time. A picture of this is shown below. C (i) Let Q(c_) be the dose concentration just before the second dose is administered intravenously. Explain why 62(0') = lim Q(t) t)c and nd a value for Q(c_) in terms of Q0 and k. (ii) Let Q(c+) be the dose concentration right after the second dose is administered intravenously. Write an expression for Q(c+) in terms of Q0 and k. (iii) Note that the concentration decays from Q(c+) according to the EDM, but with a slight twist. The twist is that the initial concentration is at t = 0 instead of t = 0. Explain why 6200 = Qo(1 + Nae-\"M when G g t