Question 1104707
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If you are going to use the {{{Ae^(-kt)}}} formula, and you want a high degree of accuracy in your answer, then you need to keep several digits of the logarithm for your calculations.<br>
One of the tutors who answered your question got an answer of 8.77 grams; a more accurate answer is 8.72 grams.  The better accuracy requires a more accurate value for the logarithm involved in the calculation.<br>
But you can avoid the logarithm problem completely by using a purely mathematical calculation, instead of using the {{{Ae^(-kt)}}} formula.<br>
The amount of the original sample after n half-lives is the original amount, multiplied by one-half raised to the power n.<br>
In this problem, the number of half-lives is 150/92.  So the amount remaining after 150 years is
{{{27(.5)^(150/92) = 8.72075}}} to 5 decimal places.<br>
There is no need with this calculation to worry about rounding errors....