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

Answer:

The concentration is increasing on #0 ≤ t < 1#

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 #K'(t) = 0#.

#0 = 8 - 8t^2#

#8t^2 = 8#

#t = +-1#

But since #t > 0#, only #t =1# is acceptable.

You will notice that whenever #t > 1#, the derivative turns negative, therefore the amount of drug in the patients system is increasing for the first hour, with #0 ≤ t < 1#.

Hopefully this helps!