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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
c%28t%29+=%285t%29%2F%28t%5E2%2B1%29+
a. graph%28+300%2C+200%2C+0%2C+8%2C+-8%2C+8%2C%285x%29%2F%28x%5E2%2B1%29%29
b. c'(t) = %285t+-+5t%5E2%29%2F%28t%5E2%2B1%29%5E2. 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 t-%3Einfinity, c%28t%29-%3E0, and so the drug concentration disappears over a long period of time.
d. You have to find the solution to the equation %285t%29%2F%28t%5E2%2B1%29+=+0.3, or equivalently, 3t%5E2+-+50t%2B3+=+0. (Use the quadratic formula.)