SOLUTION: the half life of radium is 1690 years. if 60 grams are present now, how much will be present in 670 years?

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Question 812496: the half life of radium is 1690 years. if 60 grams are present now, how much will be present in 670 years?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Basic General Model, A=Ao%2Ae%5E%28kt%29
ln%28A%29=ln%28Ao%29%2Bkt%2Aln%28e%29
ln%28A%29=ln%28Ao%29%2Bkt
k=%28ln%28A%29-ln%28Ao%29%29%2Ft
k=%28ln%281%2F2%29-ln%281%29%29%2F1690
highlight%28k=-0.000952%29

A=60%2Ae%5E%28-0.000952%2At%29
A=60%2Ae%5E%28-0.000952%2A670%29
highlight%28A=32%29, close to 31.7 grams.... This is a mistake...

CHECK:
1%2F2=1%2Ae%5E%28kt%29
ln%280.5%29=kt%2Aln%28e%29
kt=ln%280.5%29
k=%281%2F1690%29ln%280.5%29=-0.0004101 as the constant k. Believing this to be a more correct value, you should find A=60%2Ae%5E%28-0.0004101%2A670%29
highlight%28A=45%29, close to 45.4 grams. The work shown above "CHECK:" contains a mistake.