At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount A, in mg, remaining in the body is given by A=13(0.82)^t.

Question

a) What was the initial amount taken?
b) What percent of the drug leaves the body each hour?
c) How much of the drug is left in the body 6 hrs after the does is administered?
Round to two decimal places.
d) How long is it until only 1 mg of the drug remains in the body?
Round to two decimal places.

Answer 1

a) 13 mg
b) 18%
c) 13(.82)^6 = 3.95 g
d) 1 = 13(.82)^t so t=12.92 hrs