Question

The concentration of a drug in a medical patient's bloodstream is given by the formula f(t) = 2/t^2+3.

a) does the concentration of the drug increase or decrease?
b) the patient should not take a second dose until the concentration is below 1.25 milligrams per liter. How long should the patient wait before taking a second dose?

Answer 1

The concentration of the drug decreases over time. The patient should wait approximately 1.0235 units of time before taking a second dose.

Step-by-step explanation:

a) To determine whether the concentration of the drug increases or decreases, we can analyze the formula f(t) = 2/t^2+3. As time (t) increases, the denominator (t^2+3) increases, causing the concentration to decrease. Therefore, the concentration of the drug decreases over time.

b) To find out how long the patient should wait before taking a second dose, we need to find the time when the concentration is below 1.25 milligrams per liter. Setting f(t) = 1.25 and solving for t, we get t = 1.0235. Therefore, the patient should wait approximately 1.0235 units of time before taking a second dose.