Question

Medical Drugs When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient’s bloodstream after t hours is modeled by

$D\left(t\right)=50e^{-0.2t}$

How many milligrams of the drug remain in the patient’s bloodstream after 3 hours?

Short answer

27.44 ml of the drug remains in the patient’s bloodstream after 3 hours.

Step-by-step solution

Step 1. Given.

When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient’s bloodstream after t hours is modeled by

$D\left(t\right)=50e^{-0.2t}$

Step 2. To determine.

We have to find; how many milligrams of the drug remain in the patient’s bloodstream after 3 hours.

Step 3. Calculation.

According to the question, $t=3$.

We plug$t=3$ in the given function:

$$\begin{gathered} D\left(t\right)=50e^{-0.2t} \\ D\left(3\right)=50e^{-0.2\left(3\right)} \\ =27.4405818047 \\ \approx 27.44 \end{gathered}$$

Hence, 27.44 ml of the drug remains in the patient’s bloodstream after 3 hours.