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?

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) (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:

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

Use a calculator....
Answer by Boreal(15235) (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
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