Have a difficult question, may split into multiple questions.?

They don't use carbon dating on fossils. Carbon dating is only accurate for items less than 60,000 years old.

Observations of the fluctuations of the Earth's magnetic field, which leaves different magnetic fields in rocks from different geological eras. Dating a fossil in terms of approximately how many years old it is can be possible using radioisotope-dating of igneous rocks found near the fossil. Unstable radioactive isotopes of elements, such as Uranium-235, decay at constant, known rates over time (its half-life, which is over 700 million years). An accurate estimate of the rock's age can be determined by examining the ratios of the remaining radioactive element and its daughters. For example, when lava cools, it has no lead content but it does contain some radioactive Uranium (U-235). Over time, the unstable radioactive Uranium decays into its daughter, Lead-207, at a constant, known rate (its half-life). By comparing the relative proportion of Uranium-235 and Lead-207, the age of the igneous rock can be determined. Potassium-40 (which decays to argon-40) is also used to date fossils.

We do not use carbon dating for dinosaur bones. Carbon 14 (the isotope that is used for carbon dating) has a fairly short half life and is only useful for dates less than 50,000 to 70,000 years.

I assume that you are aware of atomic decay, if you are not, you should fully research it before you start in on radiometric dating. The simple explanation is that various isotopes decay (break into two different atoms) at a given rate. The time that it takes a given amount to decay to half its original quantity is called its half life. This is consistent for any quantity of the substance, i.e. if you start with 100 isotopes it will take the same amount of time to decay to 50 as 2 atoms will take to decay to 1.

So, if you know the half life of a given Isotope, the amount of it and its "daughter" isotopes (those formed by the decay), you can work out the age through some fairly straightforward formulas.

The following links will help explain this.

Edit:

You may run across claims that half lives are not known or that they can change. Neither of these are true. There are only 3 very, very short lived (half life of under a second) isotopes that are very slightly (less than 5%) effected by extreme heat. On the other hand, decay produces a great deal of energy (this is how nuclear bombs and power plants work), and if their half life were faster in the past, the earth would be a radioactive cinder.

The most common carbon dating is based on the decay rate of the carbon-14 isotope.

Small amouonts of carbon14 is being formed all the time and turned into CO2 and then into plants and things that eat plants.

All living things have a little bit of carbon14 and mostly regular carbon. The ratio is the same in all living things. When something dies, it stops taking in new carbon so the carbon14 decays (it has a half life because it is a radioactive isotope, half of any batch of new carbon14 will decay away in about 5700 years, then half of whats left will decay away in another 5700 years).

By looking at the ration of regular carbon to carbon14, you can get a pretty good estimate of time of death for the living thing with the carbon in it.

This is all based on the belief that carbon14 has always decayed at the same rate. Our current understanding of physics says that this must be, but not everybody agrees.

I don't think there is any way to prove that a million years ago carbon14 decayed at the same rate it does now. However, there is a lot of evidence and a lot of physics that say it must be that way.

Since this is on a religious forum I assume the question is related to the religious ideas of creation.

When god is involved, anything can happen. For instance, god could create things with different concentrations of carbon14 in them. He could change the cosmic rays that are a primary cause of carbon14 creation in the first place. He could build the entire earth to look EXACTLY like it would chemically if it were any age. You might doubt god would do things to be deliberately confusing, but religious people often point out that we can't really understand god or his doings because we are so limited compared to an all-knowing all-powerful immortal god.

So, did that help?

Don't be fooled by ladylion, scientists know how it works. Radiocarbon dating isn't used for dinosaur bones, but radiometric dating is (radiocarbon is a kind of radiometric dating).

In short, it works by using half-lives to see how much of an unstable material has decayed into a stable one. In the case of radiocarbon dating, the atmospheric carbon dioxide has a certain percentage of carbon-14 (which is continually made by cosmic rays striking nitrogen in the atmosphere). Plants breath that in, so the carbon in their body has the same percentage of carbon-14. Sometimes the plants are made into something, or are eaten by animals and made into something. Or just leave remains. But once that organism no longer takes in carbon, its material is at the maximum amount of carbon-14 it will ever have.

Now comes the decay part. After 5730 years half of the carbon-14 will have decayed into a stable isotope of carbon. After another 5730 years half or what's left will have decayed. And so on. We know the starting percentage of carbon-14, and the percentage of carbon-14 in the organic object being dated, then you can do simple math to find out how many years its been.

Because of it's short half-life, things older than 60,000 years cannot be dated well because the margin of error passes the precision.

The deluge would have no effect on radioactive decay. Even 850 atmospheres of pressure would not cause radioactive materials to decay faster.

Carbon dating is one form of radioisotope dating. All forms of radioisotope dating are based on the fact that radioactive atoms decay to other atoms at a predictable rate. The basic technique is to measure the amount of the original radioactive material and the amount of decay products in the sample, from which information they can calculate the age.

Carbon dating is used for organic material that is less than 70,000 years old. Older than that, and there is not enough Carbon 14 left to get an accurate measurement. Carbon dating isn't used on dinosaur bones because they are inorganic (the organic material having been replaced by minerals), and much too old.

Dinosaur fossils are dated mainly by the age of the rock strata they are found in. The absolute age of some layers can be determined by radio-isotope dating of freshly formed (volcanic) rock. Other layers are dated relative to these measurable dates.

They can't. Scientist project. They test on known samples and verify results then state that it must be true for all samples. Yes we know decay rates but we do not know if the rates fluctuate a tiny bit over time or possibly mutate. They can be 99.9 percent sure they are right but with 75 million years that means they could be off by oh 75,000 years or so and that acceptable.

My numbers are examples you can google it and get the actual accuracy that scientists state.

Here's from a scientific writing "On the other hand, the concentration of carbon-14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades.[9]. "

Leave it to scientists "precisely to within a few decades." A decades is 10 years a few decades is 30 or more years. Not exactly what I consider precise.

The short answer is this:

The half-life of carbon-14 is known. What this means is that we know how long it takes for HALF of a given quantity of carbon-14 to decay completely.

Since we know how long it takes for it to decay half way, and we have models for how much carbon-14 is in an animal before death, we know how long the animal has been dead based on how much is in it at this time.

This is a gross oversimplification, but that's the jist of it.

Also, the process is verifiable since it is used on conjunction with other methods which all agree with one another.

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A certain carbon isotope decays at a know rate.

Organic compounds have this isotope.

It's level or "activity" indicates how long ago it was formed.

16 And there were many, who had not believed the words of the prophets, who fell to the earth and became as if they were dead, for they knew that the great plan of destruction which they had laid for those who believed in the words of the prophets had been frustrated; for the sign which had been given was already at hand.

17 And they began to know that the Son of God must shortly appear; yea, in fine, all the people upon the face of the whole earth from the west to the east, both in the land north and in the land south, were so exceedingly astonished that they fell to the earth.

18 For they knew that the prophets had testified of these things for many years, and that the sign which had been given was already at hand; and they began to fear because of their iniquity and their unbelief.

19 And it came to pass that there was no darkness in all that night, but it was as light as though it was mid-day. And it came to pass that the sun did rise in the morning again, according to its proper order; and they knew that it was the day that the Lord should be born, because of the sign which had been given.

20 And it had come to pass, yea, all things, every whit, according to the words of the prophets.