Question 1130958
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The bone has lost 11% of its Carbon-14, so the percent remaining is 89%; the fraction remaining is 0.89.  The fraction remaining is the current amount, P(t), divided by the original amount, P(0).  So<br>
{{{P(t)/P(0) = 0.89}}}<br>
The given formula for the amount remaining is<br>
{{{P(t) = P(0)*e^(-0.00012t)}}}<br>
That formula is equivalent to<br>
{{{P(t)/P(0) = e^(-0.00012t)}}}<br>
So we want to solve for the number of years t in the equation<br>
{{{e^(-0.00012t) = 0.89}}}<br>
Since the exponential is base e, take the natural log of both sides of the equation:<br>
{{{-0.00012t = ln(0.89)}}}<br>
{{{t = ln(0.89)/-0.00012)}}} = 971 years to the nearest whole number