|Simplified Bern model|
So where did all the C14 go? Remember it cannot be destroyed, but it is all gone! Where?
If we consider only the top level candidates, the Biosphere on the left and the 'surface' ocean, they are not much bigger than the atmosphere. So the C14 might drop quickly, but not to zero level.
Then consider the biosphere itself. This has a rapid cycle time, except for big trees. Breathing is near instantaneous, whether animal or plant. Leaves and grasses last a year or so. Even dead organic matter is returned to the air in a short time. So even if this took the C14 , it would do less than halve it and this would come roaring back. The problem is the half life of 14 years from the graph. Nothing much except tall trees lasts 14 years, even most life on earth except man, whales and elephants and tortoises. So the biosphere cannot be the final destination of the C14 , simply because it is not final.
Now look at the right hand side. If we are to believe that the deep oceans only do things on a 1,000 year time scale, they are out of the question. The problem is that the surface ocean has only a comparable amount of CO2, so it would halve the concentration. Now look at the graph on log paper.