A Drug Is Administered to a Patient and the Concentration $c$

question 128

Essay

A drug is administered to a patient and the concentration $c$ of the drug in the bloodstream is monitored. At the time $t \geq 0$ (in minutes since the injection), the concentration (in mg/L) is given by $c ( t ) = \frac { 55 t } { t ^ { 2 } + 3 }$ .
(a) Draw a graph of the drug concentration.
(b) What eventually happens to the concentration of the drug in the bloodstream?
(c) What is the highest concentration of the drug that is reached in the patient's bloodstream? When does this occur?

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