SOLUTION: When doctors prescribe medicine, they must consider how much the drug's effectiveness will decrease as time passes. If each hour a drug is only 90% as effective as the previous hou

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Question 944816: When doctors prescribe medicine, they must consider how much the drug's effectiveness will decrease as time passes. If each hour a drug is only 90% as effective as the previous hour, at some point the patient will not be receiving enough medicine and must be given another dose. If the initial dose of medication is 300 mg, how long will it take for the initial dose to reach a level of 63 mg? Record your answer to the nearest minute.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
This drug decays to 90% each hour.

General Decay Model,y=Ie%5E%28-kt%29
I, initial amount for any t=0.

0.9=1%2Ae%5E%28-k%2A1%29, let's get the k value fast.
ln%280.9%29=-k%2A1
k=-ln%280.9%29
k=0.105


How much time to go from 300 mg to 63 mg of this drug?
300%2Ae%5E%28-0.105%2At%29=63
ln%28300%29-0.105t=ln%2863%29
-0.105t=ln%2863%29-ln%28300%29
t=%28ln%28300%29-ln%2863%29%29%2F%280.105%29

t=14.8 hours