Question

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.

Answer 1

0.56 mg

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.