A particular pain relieving medicine has a decay rate of 12% per hour. A patient was given a dose of the medicine 5 hours ago and there is currently 80 milligrams of the medicine in the patients bloodstream.

Question

After the dose was given how long must the patient wait for there to be less than 25% of the original dose of the medicine left in his or her bloodstream? Express your answer as a decimal to the nearest tenth of an hour.

Answer 1

amount at t hours = original amount * 0.88^t
so
fraction at time t = 0.88^t

Answer 2

if
0.25 = 0.88^t
then
log 0.25 = t log 0.88

Answer 3

(1 - .12)^t = .25 ... t [log(1 - .12)] = log(.25) ... t = log(.88) / log(.25)