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?

Question

Mathematics

Colton Harding

27 January, 17:10

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?

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Sanaa Maddox · 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).