Exponential decay word problem (check work)

[Jacobpm64]

At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 10(0.82)^t.

(a) What was the intial amount taken?

10 mg

(b) What percent of the drug leaves the body each hour?

18%

(c) How much of the drug is left in the body 6 hours after the dose is administered?

A = 10(0.82)⁶
A = 3.04 mg

(d) How long is it until only 1 mg of the drug remains in the body?

1 = 10(0.82)^t
1/10 = 0.82^t
ln (1/10) = t ln0.82
t = ln (1/10) / ln0.82
t = 11.6028 hours

Are these correct?

 

[Astronuc]

Certainly looks correct. It would help if one shows all work, e.g. on problem b, but the answer is correct.