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No. Any sample is undergoing change at the same time. As soon as an organism with C-14 in it dies, that clock starts counting. In one half life, half of the sample x will have disappeared. In another half life, the other half will have disappeared in the next half life. Add the two half lives, and you get 11,460 years.
Wow. Like, really, WOW! The entire physics community has been doing it all wrong for the last century? You better go look at a high school physics text, tnb. You've got that about as wrong as it's possible to get it.
In short: Half-life is the time that it takes for half the nuclei that are *in the sample* to decay. If you start with 1000 nuclei, you'll have 500 left after one half-life, 250 after two, 125 after three.....so on.