Respuesta :
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
[tex]A_{t}=10e^{-0.0173t}[/tex]
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
[tex]A_{12}=10e^{-0.0173\times12}[/tex]
[tex]A_{12}=10e^{-0.2076}[/tex]
= 10×0.81253
= 8.1 milligrams
b. In this part we have to calculate the time when A(t) = 5 milligrams
[tex]5=10e^{-0.0173\timest}[/tex]
[tex]\frac{5}{10}=e^{-0.0173t}[/tex]
0.5 = [tex]e^{-0.0173t}[/tex]
Now we take natural log on both the sides of the equation.
ln(0.5) = ln([tex]e^{-0.0173t})[/tex]
-0.69314 = -0.0173t
t = [tex]\frac{0.69314}{0.0173}[/tex]
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.
[tex]A_{7}=10e^{-0.0173\times7}[/tex]
[tex]A_{7}=10e^{-0.1211}[/tex]
= 10×0.8859
= 8.859 milligrams
