SOLUTION: 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 m
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Question 1025358: 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) = 5t/(t^2+1)
Graph the function c(t)
What is the highest concentration of the drug that is reached in the patient’s bloodstream?
What happens to the drug concentration after a long period of time?
How long does it take for the concentration to drop below 0.3 mg/L?
I need to know how to get each part a-d like the breakdown so I can understand please.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
a.
b. c'(t) = . Setting this derivative to zero to get the extreme values, we get t = 0, 1. Incidentally an absolute maximum exists at t = 1. ( c(1) = 2.5 mg/L.)
c. As , , and so the drug concentration disappears over a long period of time.
d. You have to find the solution to the equation , or equivalently, . (Use the quadratic formula.)
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