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 concent

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 concent      Log On


   

Question 1025100: 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
A.Graph the function c(t)
B.What is the highest concentration of the drug that is reached
in the patients bloodstream?
C.What happens to the drug concentration after a long period of time?
D.How long does it take for the concentration to drop below 0.3 mg/L?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A)
.
.
.
.
.
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B) C%5Bmax%5D=2.5mg%2FL
.
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C) Goes to zero as t goes to infinity
.
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D)%285t%29%2F%28t%5E2%2B1%29=0.3
50t=3%28t%5E2%2B1%29
3t%5E2-50t%2B3=0
3%28t%5E2-%2850%2F3%29t%2B%2850%2F6%29%5E2%29%2B3=3%2850%2F6%29%5E2
3%28t-25%2F3%29%5E2=625%2F3-9%2F3
3%28t-25%2F3%29%5E2=616%2F3
%28t-25%2F3%29%5E2=616%2F9
t-25%2F3=0+%2B-+sqrt%28616%29%2F3
t=25%2F3+%2B-+%282%2F3%29sqrt%28154%29
t=25%2F3%2B%282%2F3%29sqrt%28154%29
So, C%3C0.3mg%2FL when t%3E25%2F3%2B%282%2F3%29sqrt%28154%29