Question 1118557
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Scientists like to use the {{{A = Pe^(-kt)}}} formula for working problems involving half lives.  To me that is a lot of extra work, because you have to use the given information to find the k value and then use the k value to find the half life.<br>
It seems far more straightforward to simply ask how many times does the original amount need to be reduced by the decay factor to end up with half as much as you started with.<br>
For your problem, with the given information that the decay rate is 3.54% per year, we see that 96.46% of the original amount REMAINS after a year, so the decay factor is 0.9646.  Then we only need to solve<br>
{{{0.9646^x = 0.5}}}
{{{x*log((0.9646)) = log((0.5))}}}
{{{x = log((0.5))/log((0.9646)) = 19.23}}}<br>
The half life is 19.23 years.