Question 1192688
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The fraction of the original amount remaining is (1/2)^n, where n is the number of half lives.  Since 85% has been lost, 15% remains.  So<br>
{{{(1/2)^n=0.15}}}
{{{n*log(1/2)=log(0.15)}}}
{{{n=log(0.15)/log(1/2)}}}
{{{n=2.737}}} to 3 decimal places<br>
The age of the remains is 2.737 half lives:<br>
{{{2.737(5730)=15683}}} to the nearest year.<br>
Note rounding the age to the nearest whole number is not really reasonable, because radioactive decay is a statistical process which is only APPROXIMATELY exponential.<br>
ANSWER (according to the instructions): 15683 years<br>
A more correct answer: ABOUT 15700 years<br>