SOLUTION: Please help me solve this equation:
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 t
Algebra.Com
Question 1169364: Please help me solve this equation:
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 Boreal(15235) (Show Source): You can put this solution on YOUR website!
c(t)=5t/(t^2+1)
at t=0, c(t)=0
at t=1, c(t)=2.5
at t=10, c(t)=50/101
as t goes to infinity, c(t) goes to 0, consistent with the drug's gradually disappearing.
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highest concentration: this is 5t(t^2+1)^(-1)
maximum is found by setting the derivative=0.
-10t^2/(t^2+1)^2+5/(t^2+1)=0
move the term on the left to the right and divide by 5
(2t^2)/(t^2+1)^2=1/(t^2+1)
t=1, c(t)=2.5 as above.
-
5t/(t^2+1)=0.3
5t=0.3t^2+0.3
0=3t^2-50t+3
t=(1/6)(50+/-sqrt(2464)); sqrt (2464)=49.64
roots are 0.602 hours and 16.606 hours and 0.062 hours. The first is on the ascending phase right after the injection, and it is 16.61 hours before the concentration falls below 0.3 mg/L., or 16.607 hours to three decimal places.
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