This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.
A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.
However, I note that there is no beginning or ending amount given.
How am I supposed to figure out what the decay constant is?
For example, with potassium-argon dating, we can tell the age of materials that contain potassium because we know that potassium-40 decays into argon-40 with a half-life of 1.3 billion years.For example, uranium-lead dating can be used to find the age of a uranium-containing mineral.It works because we know the fixed radioactive decay rates of uranium-238, which decays to lead-206, and for uranium-235, which decays to lead-207.The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.When the isotope is halfway to that point, it has reached its half-life.There are different methods of radiometric dating that will vary due to the type of material that is being dated.The methods work because radioactive elements are unstable, and they are always trying to move to a more stable state. This process by which an unstable atomic nucleus loses energy by releasing radiation is called radioactive decay.The thing that makes this decay process so valuable for determining the age of an object is that each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life.So, if you know the radioactive isotope found in a substance and the isotope's half-life, you can calculate the age of the substance. Well, a simple explanation is that it is the time required for a quantity to fall to half of its starting value.So, you might say that the 'full-life' of a radioactive isotope ends when it has given off all of its radiation and reaches a point of being non-radioactive.