SOLUTION: Find the half-life of radium 226, which decays according to the function defined by A(t) = Ao.e^-00043t, where t is time in years.

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Question 758714: Find the half-life of radium 226, which decays according to the function defined by A(t) = Ao.e^-00043t, where t is time in years.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A%28t%29+=+A%280%29%2Ae%5E%28-.00043t%29+
At half-life, +A%28t%29+ is half of
what you started with, or +A%280%29%2F2+
+A%280%29%2F2+=+A%280%29%2Ae%5E%28-.00043t%29+
Divide both sides by +A%280%29+
+1%2F2+=+e%5E%28+-.00043t+%29+
Take the natural log of both sides
+ln%28+.5+%29+=+-.00043t+
+-.6931+=+-.00043t+
+t+=+.6931+%2F+.00043+
+t+=+1611.861+ yrs
check:
+.5+=+e%5E%28+-.00043t+%29+
+.5+=+e%5E%28+-.00043%2A1611.861+%29+
+.5+=+e%5E%28+-.6931+%29+
+.5+=+.50002+
close enough