Question

At time (t) hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 14(0.8)^t.. What percent of the drug leaves the body each hour?. How much of the drug is left in the body 2 hours after the dose is administered? How long is it until only 1 mg of the drug remains in the body?

Answer 1

1)we calculate the amount of the drug is left in the body 2 hours after the dose is administered.
t=2
A(t)=14(08)^t
A(t)=14(0.8)²=14(0.64)=8.96

Answer: after of two hours the amount of drug left in te body is 8.96 mg.

2)we calculate the time required to stay in the body 1 mg of drug.

A(t)=1
14(0.8)^t=1   
ln [14(0.8)^t]=ln1
ln14+tln(0.8)=0
tln(0.8)=-ln 14
t=-ln 14 / ln (0.8)
t=11.8267...≈11.83

Answer: the time required is 11.83 hours  (≈11 hours, 49 minutes, 48 seconds).