SOLUTION: given A(t)=Ao e^-0.00023t is a proper model for radioctive decay, find the halflife (years)

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Question 601067: given A(t)=Ao e^-0.00023t is a proper model for radioctive decay, find the halflife (years)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A%28t%29+=+A%5B0%5De%5E%28rt%29

50+=+100%2Ae%5E%28-0.00023t%29

50%2F100+=+e%5E%28-0.00023t%29

0.5+=+e%5E%28-0.00023t%29

ln%280.5%29+=+ln%28e%5E%28-0.00023t%29%29

ln%280.5%29+=+-0.00023t%2Aln%28e%29

ln%280.5%29+=+-0.00023t%2A%281%29

ln%280.5%29+=+-0.00023t

ln%280.5%29%2F-0.00023+=+t

-0.693147180559945%2F-0.00023+=+t

3013.68339373889+=+t

t+=+3013.68339373889


So the half-life is roughly 3013.68339 years.