#2 (Stewart ², #34 p. 77) A drug is administered once a day. Suppose C₁ is the concentration of the drug in the bloodstream (in µg/mL) after n days (just after the dose is administered), 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. The drug concentration can be modeled by Cn Cn-1(1 k) + A where Co is the initial dose that is administered. a) Imagine you explain to another student in this class why this DDS describes the drug concentration. Explain each of the terms of the updating function. b) Write the recursive equation if A = 80 µg/mL and k = and simplify. Is this a model with a linear updating function? Why or why not? c) If the initial concentration is Co= 120 µg/mL, find the explicit solution (if it exists) and use either the explicit solution or the recursive DDS to find C₁, C₂, and C3.

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#2 (Stewart², #34 p. 77) A drug is administered once a day. Suppose C₁ is the concentration of the drug
in the bloodstream (in µg/mL) after n days (just after the dose is administered), 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. The drug concentration can be modeled by
Cn
Cn-1(1 k) + A
where Co is the initial dose that is administered.
a) Imagine you explain to another student in this class why this DDS describes the drug
concentration. Explain each of the terms of the updating function.
b) Write the recursive equation if A = 80 µg/mL and k = and simplify. Is this a model with a
linear updating function? Why or why not?
c) If the initial concentration is Co= 120 µg/mL, find the explicit solution (if it exists) and use either
the explicit solution or the recursive DDS to find C₁, C₂, and C3.
Transcribed Image Text:#2 (Stewart², #34 p. 77) A drug is administered once a day. Suppose C₁ is the concentration of the drug in the bloodstream (in µg/mL) after n days (just after the dose is administered), 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. The drug concentration can be modeled by Cn Cn-1(1 k) + A where Co is the initial dose that is administered. a) Imagine you explain to another student in this class why this DDS describes the drug concentration. Explain each of the terms of the updating function. b) Write the recursive equation if A = 80 µg/mL and k = and simplify. Is this a model with a linear updating function? Why or why not? c) If the initial concentration is Co= 120 µg/mL, find the explicit solution (if it exists) and use either the explicit solution or the recursive DDS to find C₁, C₂, and C3.
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