KCC's Quizzes AQQ245 on Fossil Dating with Carbon14

1/2 life of 5568  implies that after 5568 years, there is only half of the original content left. 
Since the content is about one quarter of its original content, that makes exactly 2 half lifes, or that your mammoth failed to meet Homer, in the 800 BC (roughly 3000 years ago) or the construction of the pyramids in Egypt, but died more about like  11136 years ago.

As for the concentration of C12 of today, that does not matter since we compare the ratio of the today residual C14 to C12 from the bone with respect to the initial ratio which was in vigor at the time of the living... died. Since its death, the bone didn't capture any new Carbon and thus, as a photo that we would have taken then, it is unaffected by today ratio. 

Thanks for your replay vanderghast ! Answer to question 1 is indeed correct (11136 years). I don't know if there as still mammoth alive at the time of Homer or pyramids constrution in Egypt... May be in Siberia? 

On question 2, I agree there can be many assumption with unknowns like how fast and where (? only in the upper atmosphere level)  the C12 atoms are transformed in C14? By assuming the C12 generated by the human actvitiies, thus only in the very last 50 years and by assuming those additional C12 have not the time to reach the upper atmoshere layer, we can then extrapolate the C14/C12 ratio appears much less than it should be; thus giving a longer age

Thanks for your replay vanderghast ! Answer to question 1 is indeed correct (11136 years). I don't know if there as still mammoth alive at the time of Homer or pyramids constrution in Egypt... May be in Siberia? 

On question 2, I agree there can be many assumption with unknowns like how fast and where (? only in the upper atmosphere level)  the C12 atoms are transformed in C14? By assuming the C12 generated by the human actvitiies, thus only in the very last 50 years and by assuming those additional C12 have not the time to reach the upper atmoshere layer, we can then extrapolate the C14/C12 ratio appears much less than it should be; thus giving a longer age

I agree,

somehow.

I find it analogous to discharging a capacitor. Parameters:  Vc0, the initial voltage inside the capacitor, is like the initial ratio C14/(C12+C14); the time of discharge is the time since death of the living part we analyzed, the RC constant is similar to the decay speed of C14, and finally, Cvt, the tested actual voltage at the capacitor is the actual ratio C14/(C12+C14). We have two parameters left: Vc0, the initial voltage or the initial ratio, and t, the time since we started the discharge. Giving one of these allows us to find the other.

But.

For a dead part, that component does not "refill" itself with "today" Carbon of any kind. Assuming that C14 was in a steady proportion (what is destroyed by fission equals what was created in the atmosphere) we were able to assume Vc0. But since the Carbon source of the new carbon for C02 comes mostly from a carbon source depleted of C14  (long time dead living parts, as coal or oil) we won't be able to use that technique for "dead" parts not older than about 200 years. It is unfortunate that unlike Uranium contained in a Zircon crystal, we can count the Uranium atoms AND the Lead atoms to get the initial total number of Uranium atoms.

Excellent analogy with capacitor charging vanderghast ! And I agree with you, C14 method is somehow imprecise since many assumptions were made. And the mid-life tiime had been updated many times as well.