Math 1111

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Worksheet 7

Concentration of a drug.  The concentration of a drug in a medical patient’s bloodstream is given by the formula , where the input t > 0 is in hours and the output is in milligrams per liter. 

  • Graph the function and provide a copy of the graph.  If you are using software, you will want to remember first that the function is only valid for t >0.  Second you cannot graph with the variable t.  Substitute the variable x for t.  In geogebra, you may choose to use the if statement.  Here is how you can enter it in geogebra  f(x) = if(x > 0, 5/(x2+1))
  • Use the graph to discuss what happens to the concentration of the drug over time.
  • What is the concentration after 30 minutes? 1 hour? 6 hours? (Note the units for time above are hours so make sure you convert to hours.  You can use the graph or plug in the values.)
TimeConcentration
30 minutes 
1 hour 
6 hours 
  • The patient should not take a second dose until the concentration is below 1.5 milligrams per liter.  How long should the patient wait before taking a second dose?  I want you to solve the equation.  Set the function (5/(t2+1)) equal to 1.5 and solve for t.  Check your answer on the graph. 
  • When will the concentration equal 0?  Explain your answer in terms of the graph of this rational function and asymptotes.