invalidating a deed of trust - Radiocarbon dating example problem
The halflife of carbon 14 is 5730 ± 30 years, and the method of dating lies in trying to determine how much carbon 14 (the radioactive isotope of carbon) is present in the artifact and comparing it to levels currently present in the atmosphere.
Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.
Radiocarbon dating (usually referred to simply as carbon-14 dating) is a radiometric dating method.
Carbon has two stable, nonradioactive isotopes: carbon-12 (12C) and carbon-13 (13C).
There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth.
Since carbon is fundamental to life, occurring along with hydrogen in all organic compounds, the detection of such an isotope might form the basis for a method to establish the age of ancient materials.
Libby, a Professor of Chemistry at the University of Chicago, predicted that a radioactive isotope of carbon, known as carbon-14, would be found to occur in nature.
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.