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 1154570: 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)=A0e^(kt)
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.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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that over each hour, 25% of the amount present at the beginning of the hour is eliminated.
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A%28t%29=A%5Bo%5De%5E%28kt%29
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0.75=1.00e%5E%281%2Ak%29
e%5E%28k%29=0.75
ln%28e%5Ek%29=ln%280.75%29
k=ln%280.75%29
highlight%28k=-0.2877%29


highlight%28A%28t%29=A%5Bo%5De%5E%28-0.2877t%29%29
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You could round to k=-0.29 if you want.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
+t+=+1+ hr
+.75A%5B0%5D+=+A%5B0%5D%2Ae%5E%28k%2A1+%29+
+.75+=+e%5Ek+
+k+=+ln%28+.75+%29+
+k+=+-.28768+
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+.5A%5B0%5D+=+A%5B0%5D%2Ae%5E%28+k%2At+%29+
+.5+=+e%5E%28+k%2At+%29+
+ln%28+.5+%29+=+k%2At+
-+.69315+=-+.28768t+
+t+=+2.4094+
+t+=+2.41+ ( rounded off )
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check the math & get a 2nd opinion if needed