Answer:
 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.
There are 0.55 milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours.
A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
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.
[tex]\rm M(t)=50 (e^-0.75t)[/tex]
The milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours is;
[tex]\rm M(t)=50 (e^{-0.75t})\\\\t =6\\\\M(t)=50 (e^{-0.75 \times 6})\\\\M(t)=50 (e^{-4.5})\\\\ M(t)=50 \times 0.0111\\\\M(t)=0.55 mg[/tex]
Hence, there are 0.55 milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours.
Learn more about exponental function here;
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