How do you find on what time interval is the concentration of the drug increasing if suppose a certain drug is administered to a patient, with the percent of concentration in the bloodstream t hr later given by #K(t)= 8t / (t^2 + 1)#?
1 Answer
Apr 15, 2018
The concentration is increasing on
Explanation:
You will need to start by differentiating.
#K'(t) = (8(t^2 + 1) - 8t(2t))/(t^2 + 1)^2#
#K'(t) = (8t^2 + 8 - 16t^2)/(t^2 + 1)^2#
#K'(t) = (8 - 8t^2)/(t^2 + 1)#
This will have a critical number when
#0 = 8 - 8t^2#
#8t^2 = 8#
#t = +-1#
But since
You will notice that whenever
Hopefully this helps!