When a patient is given medication, the drug enters the bloodstream. The rate at which the...

 

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When a patient is given medication, the drug enters the bloodstream. The rate at which the drug is metabolized and eliminated depends on the particular drug. For the antibiotic ampicillin, approximately 40% of the drug is eliminated every hour. A typical dose of ampicillin is 250 mg. The quantity Qof the drug remaining in the bloodstream at time zis approximately a4=250e 0.5t mg. a) Find Q0) and g(O) and explain their meanings in terms of this scenario. b) Use your graphing calculator to make a sketch of aa. In words, describe the graph using terminology from Ch. 3. C) The function Q is not quite as realistic as we would like - particularly at the beginning of the dosage. Use your graphing calculator to make a sketch of the function AD=250 te 0.52, Describe this graph and explain how this function does a better job at modeling the behavior of the drug in the blood stream. (Note that A is in a class of functions referred to as surge functions.) d) Which model Q or A allows for the greatest amount of ampicillin in the bloodstream? Why is the amount for A more realistic? e) Using calculus, find the time at which Agis greatest. What is the maximum value of A? When a patient is given medication, the drug enters the bloodstream. The rate at which the drug is metabolized and eliminated depends on the particular drug. For the antibiotic ampicillin, approximately 40% of the drug is eliminated every hour. A typical dose of ampicillin is 250 mg. The quantity Qof the drug remaining in the bloodstream at time zis approximately a4=250e 0.5t mg. a) Find Q0) and g(O) and explain their meanings in terms of this scenario. b) Use your graphing calculator to make a sketch of aa. In words, describe the graph using terminology from Ch. 3. C) The function Q is not quite as realistic as we would like - particularly at the beginning of the dosage. Use your graphing calculator to make a sketch of the function AD=250 te 0.52, Describe this graph and explain how this function does a better job at modeling the behavior of the drug in the blood stream. (Note that A is in a class of functions referred to as surge functions.) d) Which model Q or A allows for the greatest amount of ampicillin in the bloodstream? Why is the amount for A more realistic? e) Using calculus, find the time at which Agis greatest. What is the maximum value of A?

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