[UnbelievingScumOnTheOtherSide]

No. Let's say baseline C-14 is 10,000 parts/million.

5000 parts = 5700 years
2500 parts = 11400 years
1250 parts = 22800
625 parts = 45,500

and so on.

Uh no. First, 10,000ppm (1%) is way too high. We'd be glowing in the daytime. But you also don't double the years.

5000 parts = 5700 years
2500 parts = 11400 years
1250 parts = 17100
625 parts = 22800
312 parts = 28500
156 parts = 34200
78 parts = 39900
39 parts = 45600
19.5 parts = 51300
9.75 parts = 57000
...

[MeanWestTexan]

As stated, the numbers were arbitary just to show that the process worked for longer than 11,700 years or whatever the question was.

[MeanWestTexan]

Just for accurracy, the actual reference level is 1.18×10-12 C-14 atom per C-12 atom (one C-14 for 848 billion C-12 atoms). The better-equipped radiocarbon dating laboratories using the conventional gas or scintillation counting technique are capable of detecting concentrations of C-14 as low as 1.4×10-15 (one atom of C-14 per 700 thousand billion C-12 atoms) --- giving an outside accepted range of 55,000 years(although some go higher, and most say 40,000, due to contamination).