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Jhart1234
Jhart1234
07.12.2020 • 
Mathematics

Carlos has taken an initial dose of a prescription medication. The relationship between the elapsed time ttt, in hours, since he took the first dose, and the amount of medication, M(t)M(t)M, left parenthesis, t, right parenthesis, in milligrams (\text{mg}mgstart text, m, g, end text), in his bloodstream is modeled by the following function.
M(t)=20\cdot e^{{-0.8t}}M(t)=20⋅e
−0.8t
M, left parenthesis, t, right parenthesis, equals, 20, dot, e, start superscript, minus, 0, point, 8, t, end superscript
In how many hours will Carlos have 1\text{ mg}1 mg1, start text, space, m, g, end text of medication remaining in his bloodstream?
Round your answer, if necessary, to the nearest hundredth.

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