Hi, all. Please teach me a question about exponential decay.

The question is "You buy a supposedly genuine 2000 year old eggshell of the extinct giant elephant bird Aepyornis, however you are not sure of its authenticity. You useyour Liquid Scintillation Counter to work out that the proportion of carbon-14, C14, in a sample of the eggshell is 0:883% of the proportion that would naturally occur at the time it was laid. Using methods from the notes, make a decision whether the eggshell authentic or not. The decay constant of C14 is r= 0.000125 per year."

I solved this by using M/M0 = e^rt, and r = 0.000125. So, e^(-0.000125*2000) = 0.778801....

C14 decreases as time increases. But, 0.883%, in other words, approximately 0.00883 of the eggshell was C14 as naturally occured.

If the eggshell is authentic, that means that the proportion of C14 has increased which yield contradiction. Thus, the eggshell is not authentic.

May I ask if I am correct?

Thanks a lot!

Have a great day.