A Particular pain relieving medicine has a decay rate of 24% an hour. A patient was given a dose of the medicine 5 hours ago and there is currently 74mg of the medicine in the patients bloodstream.

Question

Q: What was the Origional dose of the medicine? ________ milligrams.
Q How long will the patient need to wait for there to be less than 25% of the original dose of the medicine left in the bloodstream? _______hours. (to the nearest tenth of an hour)

Answer 1

after t hours, starting with A mg, the amount remaining is

A*.76^t

So, to find the original dose, solve

A*.76^5 = 74

To get to 25%, you want

.76^t = .25