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Answer:
a. 8.1 milligrams
b. 40.07 hours
c. 8.859 milligrams
Explanation:
If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time can be modeled by
Where A(t) = amount of Valium remaining in the blood after t hours
t = time or duration after the drug is taken
a. we have to calculate the amount of drug remaining in the bloodstream after 12 hours
= 10×0.81253
= 8.1 milligrams
b. In this part we have to calculate the time when A(t) = 5 milligrams
0.5 =
Now we take natural log on both the sides of the equation.
ln(0.5) = ln(
-0.69314 = -0.0173t
t =
t = 40.0658
≈ 40.07 hours
c. In this part we have to calculate the rate, by which amount of drug will decay in the bloodstream after 7 hours.
= 10×0.8859
= 8.859 milligrams