A drug is administered to a patient, and the concentration of the drug in the bl

Question

A drug is administered to a patient, and the concentration of the drug in the bloodstream is monitored. At time t > 0 (in hours since giving the drug), the concentration (in mg/L) is given by c(t) = 8t/t2+1. Graph the function c with a graphing device. (Round your answers to two decimal places.) What is the highest concentration of drug that is reached in the patient's bloodstream? What happens to the drug concentration after a long period of time? The concentration of the drug in the bloodstream goes to 0 mg/L. Nothing, the concentration of the drug remains constant throughout its time in the bloodstream. The concentration of the drug in the bloodstream is naturally restored to its highest level. The concentration of the drug in the bloodstream is reduced by 50%. How long does it take for the concentration to drop below 0.2 mg/L?

Explanation / Answer

0.2 = 8t/(t^2+1)

or

t^2 + 1 - 40t = 0

or

t = 39.97 hrs

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