Question

The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 14 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 4 hr after dosage.
a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours after a 1000-mg dosage.
b) Estimate the concentration of the drug 3 hr after a 1000-mg dosage.
c) To relieve a fever, the concentration of the drug should go no lower than 4 mcg/mL. After how many hours will a 1000-mg dosage drop to that level?
k = ________(Round to three decimal places as needed.)

Answer 1

Answer:

Step-by-step explanation:

14 = 1000 $e^{ k*1}$

.014 = $e^{k*1}$

ln(.014) = k ln(e)

k = -4.268

~~~~~~~~~~~~~~~~~~

after 3 hrs

1000 $e^{ -4.268*3}$

0.00274

~~~~~~~~~~~~~~~

4 = 1000 $e^{ -4.268*t}$

.004 =  $e^{ -4.268*t}$

ln(.004)/-4.268 = t

t = 1.29368 hrs