SOLUTION: A drug is eliminated from the body through the kidney in such a way that over each hour, 25% of the amount present at the beginning of the hour is eliminated. Let t be the amount o

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Question 1154569: A drug is eliminated from the body through the kidney in such a way that over each hour, 25% of the amount present at the beginning of the hour is eliminated. Let t be the amount of time (in hours) since the drug was first taken, and A0 the initial amount of the drug in the body. The amount of drug present in the body after t hours is given by:
A(t)=A0ekt
where k is some constant. How long does it take before the amount of drug in the body is half of the initial amount (Round answer to two decimal places). Do not include units with your answer.
Answer by greenestamps(13207) About Me  (Show Source):
You can put this solution on YOUR website!


The instructions don't say to find the value of the constant k, or to use the given formula. So I will use a simpler formula.

The amount remaining decreases to 75% of its initial value over each hour:
A%28t%29+=+A%280%29%28.75%29%5Et

We need to find the number of hours t required for the amount to drop to half the original amount:

A%280%29%2F2+=+A%280%29%28.75%29%5Et
0.5+=+.75%5Et
log%28%280.5%29%29+=+t%2Alog%28%280.75%29%29
t+=+log%28%280.5%29%29%2Flog%28%280.75%29%29 = 2.40942..., or, to 2 decimal places, 2.41.

ANSWER: 2.41 hours