Dinosaur bones dated with carbon-14

This escaped my notice at the time (2012 August). We should definitely carbon date more fossils and ignore calls that this is a waste of time because we already know that fossils cannot contain carbon-14 except as a contaminant.

Coal and diamonds both contain radioactive carbon despite supposedly being too old. The half-life of carbon-14 is 5730 years. So after 5700 years there is half the original amount of carbon-14 left. After 11500 years a quarter of the original amount. If we assume all the carbon in an object is carbon-14 (it is however only a fraction) we can get an extreme upper bound on how old it can be (carbon-14 decays into nitrogen so the known presence of carbon-12 lowers this upper bound considerably). If we measure any carbon-14 we know it must be younger than the extreme upper bound age, though it could be much younger.

So carbon-14 has been found in

1. Coal
2. Diamonds
3. Dinosaurs

All of which are claimed to be older than what they possibly can be. This refutes the argument for an ancient earth. The only response possible is contamination.