Olivia has taken an initial dose of a prescription medication.

The relationship between the elapsed time T, in hours, since she took the first dose, and the amount of medication M (t), in milligrams (mg), remaining in her bloodstream is modeled by the following function.

M (t) = 50 (e^-0.75t)

How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours?

Round your answer, if necessary, to the nearest hundredth.

Question

Cohen Duarte

Mathematics

19 June, 05:03

Olivia has taken an initial dose of a prescription medication.

The relationship between the elapsed time T, in hours, since she took the first dose, and the amount of medication M (t), in milligrams (mg), remaining in her bloodstream is modeled by the following function.

M (t) = 50 (e^-0.75t)

How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours?

Round your answer, if necessary, to the nearest hundredth.

+4

Answers (1)

Know the Answer?

Emmalee Oconnor · Answer 1

0.56 mg

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

M (6) = 50 (e^ (-0.75·6)) = 50e^-4.5 ≈ 0.56

Olivia will have about 0.56 mg of medication remaining in her blood.