Final answer:
The concentration will be 0.5 mg/L at approximately 0.481 hours and 39.518 hours after the drug is administered.
Step-by-step explanation:
The concentration of the drug in the bloodstream hours after it is administered is modeled by the function c(t) = 20t/(t^2+4). To determine when the concentration will be 0.5 mg/L, we can set up the equation:
0.5 = 20t/(t^2+4)
Multiplying both sides by (t^2+4), we get:
0.5(t^2+4) = 20t
Dividing both sides by 0.5, we have:
(t^2+4) = 40t
Rearranging the equation:
t^2 - 40t + 4 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2-4ac))/(2a)
Applying the quadratic formula with a = 1, b = -40, and c = 4, we find two possible solutions for t:
t = 39.518 or t = 0.481
Therefore, the concentration will be 0.5 mg/L at approximately 0.481 hours and 39.518 hours after the drug is administered.