SOLUTION: A particular antibiotic is eliminated from the blood at a rate of 15% per hour what is the half life of the drug? How many hours does it take for a 100milligram dose to decrease to

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Question 1007706: A particular antibiotic is eliminated from the blood at a rate of 15% per hour what is the half life of the drug? How many hours does it take for a 100milligram dose to decrease to 1milligram in the blood?
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
p, starting quantity
y, resulting quantity after some time t
t, some time passage
k, rate constant
MODEL in general: y=pe%5E%28-kt%29

Loss of 15% in one hour means
0.85=1%2Ae%5E%28-k%2A1%29
take log of each side and solve for.....
highlight_green%28k=-ln%280.85%29%29.

More specific model is y=pe%5E%28-0.1625t%29.
To answer the question, let p=100,y=1,solve for t.

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Also, half-life was asked. You can use the specific model to find this.
y=pe%5E%28-0.1625t%29
ln%28y%29=ln%28p%29-0.1625t
ln%28y%2Fp%29=-0.1625t
ln%28p%2Fy%29=0.1625t
ln%282%29=0.1625t
highlight%28t=ln%282%29%2F0.1625%29