SOLUTION: A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 36 hours, 50 mg of the substance remains. How many milligrams will remain after 5

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Question 1055965: A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 36 hours, 50 mg of the substance remains. How many milligrams will remain after 52 hours ?
_________ mg
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 36 hours, 50 mg of the substance remains.
y = a*b^x
50 = 100*b^36
b = 0.5^(1/36)
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How many milligrams will remain after 52 hours ?
f(x) = 100*(0.5)^(x/36)
f(52) = 100*(0.5)^(52/36) = 36.74 mg
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+A%5B0%5D%2Ae%5E%28-r%2At%29+
+A%5B0%5D+=+100+ mg
+A+=+50+ mg
+t+=+36+ hrs
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+50+=+100%2Ae%5E%28-r%2A36%29+
+1%2F2+=+e%5E%28-r%2A36%29+
Take the natural log of both sides
+ln%281%2F2%29+=+-r%2A36+
+-.6931+=+-r%2A36+
+r+=+.01925+
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+t+=+52+
+A+=+100%2Ae%5E%28-.01925%2A52%29+
+A+=+100%2Ae%5E%28-1.0012%29+
+A+=+100%2A.3675+
+A+=+36.75+
36.75 mg remain after 52 hrs
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Hope I got it