After taking a certain antibiotic, the concentration (C) of the drug in the patient's bloodstream is given by C(x)=(0.04t)/(t2−2), where t is the time (in hours) after taking the antibiotic. How many hours after the antibiotic will its concentration be 0.04 units?
+36923 First, that is not a concentration dimension. (.04 units)
But I will assume that you are asking when will C(x) = .04
.04 = .04t / (t^2-2) Multiply both sides by t^2-2
.04t^2 -.08 =.04t
.04t^2-.04t-.08=0 Multiply both sides by 100 (to make it easier to work with it)
4t^2 - 4t - 8 = 0 Now divide by 4
t^2-t-2 = 0
(t-2)(t+1) = 0 means either t=2 or -1 hours -1 hours is not possible, so the only REAL answer is t=2 hours
