SOLUTION: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour. To the nearest tenth, what is the half-life of the drug?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour. To the nearest tenth, what is the half-life of the drug?      Log On


   

Question 1138573: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour. To the nearest tenth, what is the half-life of the drug?
Found 2 solutions by greenestamps, Boreal:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since it decays by 17% per hour, the amount remaining gets multiplied by 100-17 = 83% each hour. The amount remaining after t hours is then the initial amount, multiplied by 0.83 t times:

300%280.83%29%5Et

The problem asks for the half-life -- i.e., the amount of time it takes for the original amount to be reduced to half.

300%280.83%29%5Et+=+150
0.83%5Et+=+0.5
t%2Alog%28%280.83%29%29+=+log%28%280.5%29%29
t+=+log%28%280.5%29%29%2Flog%28%280.83%29%29

Use a calculator....

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The decrease is 17% per hour or (0.83)^t, where t is number of hours.
So want 0.5=0.83^t
ln of both sides
-0.693=t ln (0.83)
t=3.719 hours or 3.7 hours