Question

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?
Select one:
a. 2 hours
b. 4 hours
c. 3 hours
d. 5 hours

Answer 1

Answer:

The required time is 2 hours

option (a) is correct

Step-by-step explanation:

The concentration (C) of the drug in the patient's bloodstream is given by

$C(t)=\frac{0.04t}{t^2-2}$..........(1)

when C=0.04, from equation (1)

$0.04=\frac{0.04t}{t^2-2}$

$1=\frac{t}{t^2-2}$

$t^2-2=t$

$t^2-t-2=0$

$(t-2)(t+1)=0$

$t=2,-1$

But time cannot be negative

$\implies\:t=2\:hours$