Question

When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after hours is modeled by

D(t) = 90e⁻⁰.²ᵗ
How many milligrams of the drug remain in the patient's bloodstream after 5 hours? (Round your answer to one decimal place.)

Answer 1

Approximately 33.1 milligrams of the drug remain in the patient's bloodstream after 5 hours.

Step-by-step explanation:

To find the amount of milligrams of the drug remaining in the patient's bloodstream after 5 hours, we can substitute t=5 into the given equation.

D(t) = 90e⁻⁰.²ᵗ

D(5) = 90e⁻⁰.²(5)

D(5) = 90e⁻¹

Using a calculator, we can evaluate e⁻¹ which is approximately 0.368.

D(5) = 90 * 0.368

D(5) = 33.12

Therefore, approximately 33.1 milligrams of the drug remain in the patient's bloodstream after 5 hours.