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A dose of morphine is absorbed from the bloodstream of a patient at a rate proportional
to t


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A dose of morphine is absorbed from the bloodstream of a patient at a rate proportional
to the amount in the bloodstream.
(a) Write a dierential equation for M????t, the amount of morphine in the patient?s
bloodstream, using k as the constant proportionality.
(b) Assuming that the initial dose of morphine is M0, solve the initial value problem
to nd M????t. Use the fact that the half-life for the absorption of morphine is
two hours to nd the constant k.
(c) Suppose that a patient is given morphine intraveneously at the rate of 3 milligrams
per hour. Write a dierential equation that combines the intraveneous
administration of morphine with the body?s natural absorption.
(d) Find any equilibrium solutions and determine their stability.
(e) Assuming that there is initially no morphine in the patient?s bloodstream, solve
the initial value problem to determine M????t. What happens to M????t after a very
long time?
(f) To what rate should a doctor reduce the intraveneous rate so that there is
eventually 7 milligrams of morphine in the patient?s bloodstream?

 


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A dose of morphine is absorbed from the bloodstream of a patient at a rate proportional
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This paper was answered on 14-Oct-2020

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