In a radioactive sample, the signal (the amount of radioactivity) that is measured is going to be given by
A =
A0e-kt/5730,
where
A0 is a constant related to the amount of C14 that was initially present, and
k is the natural log of 2. If we assume that the same amount of C14 is always initially present in every sample (in real life this isn't true, but shouldn't affect the results here by more than an order of magnitude or so), then we have
diamond:
Ad =
A0e-k58000/5730
something else:
Ase =
A0e-k5800/5730
Thus, dividing:
Ase/
Ad =
ek(58000-5800)/5730=
ek52200/5730=
e9k=512
Thus, the something else in your example has 512 times the signal of the diamond.
Hope this helps.
Edited by Chiroptera, : Forgot the correct factor in the exponent.
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