Question

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 95% 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 was 250 mg, what will the level of the dose be after 3 hours?

Answer 1

Answer:

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

Step-by-step explanation:

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