SOLUTION: an isotope of strontium 90 has a half life of 38 years. if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?

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Question 609841: an isotope of strontium 90 has a half life of 38 years. if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?
Answer by nerdybill(7384) About Me  (Show Source):
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an isotope of strontium 90 has a half life of 38 years. if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?
exponential growth/decay equation
A+=+Aoe%5E%28kt%29
where
A is amount after time t
Ao is the initial amount
k is the growth/decay constant
t is time
.
From: "an isotope of strontium 90 has a half life of 38 years." we can determine k:
.5Ao+=+Aoe%5E%28k%2A38%29
dividing both sides by Ao:
.5+=+e%5E%28k%2A38%29
ln%28.5%29+=+38k
ln%28.5%29%2F38+=+k
-.01824+=+k
.
Now, we can answer:
if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?
starting with:
A+=+Aoe%5E%28-.01824t%29
A+=+500e%5E%28-.01824%2A19%29
A+=+500%28.7071%29
A+=+354.55 mg