Question

g 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 with the exponential decay function A ( t ) = 10 e − 0.0173 t where t is in hours. a . How much Valium remains in the person's bloodstream 12 hours after taking a 10 -mg dose? Round to the nearest tenth of a milligram. mg b . How long will it take 10 mg to decay to 5 mg in a person's bloodstream? Round to two decimal places. hours c . At what rate is the amount of Valium in a person's bloodstream decaying 7 hours after a 10 -mg dose is taken. Round the rate to three decimal places. A ' ( 7 ) =

Answer 1

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

$A_{t}=10e^{-0.0173t}$

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

$A_{12}=10e^{-0.0173\times12}$

$A_{12}=10e^{-0.2076}$

                = 10×0.81253

                = 8.1 milligrams

b. In this part we have to calculate the time when A(t) = 5 milligrams

$5=10e^{-0.0173\timest}$

$\frac{5}{10}=e^{-0.0173t}$

0.5 = $e^{-0.0173t}$

Now we take natural log on both the sides of the equation.

ln(0.5) = ln($e^{-0.0173t})$

-0.69314 = -0.0173t

t = $\frac{0.69314}{0.0173}$

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.

$A_{7}=10e^{-0.0173\times7}$

$A_{7}=10e^{-0.1211}$

              = 10×0.8859

              = 8.859 milligrams