SOLUTION: A particular pain relieving medicine has a decay rate of 16 % per hour. A patient was given a dose of the medicine 7 hours ago and there is currently 66 milligrams of the medicine

Algebra ->  Finance -> SOLUTION: A particular pain relieving medicine has a decay rate of 16 % per hour. A patient was given a dose of the medicine 7 hours ago and there is currently 66 milligrams of the medicine       Log On


   

Question 1040382: A particular pain relieving medicine has a decay rate of 16 % per hour. A patient was given a dose of the medicine 7 hours ago and there is currently 66 milligrams of the medicine in the patients bloodstream.
What was the original dose of the medicine? _________ milligrams
How long will the patient need to wait for there to be less than 25 % of the original dose of the medicine left in their bloodstream?
Express your answer as a decimal to the nearest tenth of an hour. _______hours
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the original dose of medicine
+66+=++d%2A%28+1+-+.16+%29%5E7+
+66+=+d%2A.84%5E7+
+66+=+.2951d+
+d+=+223.66+ mg original dose
-------------------------------
+223.66%2F4+=+223.66%2A.84%5Et+
+.84%5Et+=+1%2F4+
Take the log of both side
+t%2Alog%28%28+.84+%29%29+=+log%28%28+.25+%29%29+
+-.07572t+=+-.6021+
+t+=+7.9511+
In 8 hrs less than 25% of the original dose will
be in the bloodstream
----------------------
You might want a 2nd opinion on these, also