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If the half life is 5700 years, how do you find the percentage of original carbon-14 that remains in a sample after 2476 years have passed?

Answer 1

I get #74.1%# of the original amount remaining.

Well, if the half-life of #""14^C# is #5700# years, then that means after #5700# years have happened, there will be half of the original amount, i.e. #50%# of the original amount of #""14^C# left.

So, after #2476# years, the sample of #""14^C# has evolved:

#2476/5700~~43.4%# of a half-life

A rule to remember is that if #n# is the number of half-lives elapsed, there will be #100/(2^n)%# of the original amount of substance remaining. For the source of this information, click here.

So here, #n=43.4%=0.434#. Therefore, there will be

#100/(2^0.434)#

#~~100/1.35#

#~~74.1%# of the original amount remaining.

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Answer 2

Oliver Antoine

[ \text{Percentage remaining} = \left( \frac{1}{2} \right)^{\frac{2476}{5700}} \times 100 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.