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(Solution Library) A drug is administered intravenously at constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with

Question: A drug is administered intravenously at constant rate of \(r\) mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality \(\alpha>0\).

  1. Solve a differential equation for the quantity, \(Q_{1}\) in milligrams, of the drug in the body at time \(t\) hours. Assume there is no drug in the body initially. Your answer will contain \(r\) and \(\alpha\). Graph Q against \(t\). What is Q \(\infty\), the limiting long-run valued \(Q\) ?
  2. What effect does doubling r have on Q \(\infty\) ? What effect does doubling \(r\) have on the time to reach half the limiting value, \(\frac{1}{2} Q \infty ?\)
    c.) What affect does doubling o have on \(Q \infty\) ? On the time to reach \(\frac{1}{2}\) Q \(\infty\) ?
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    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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