At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.
When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.
Many factors limit the accuracy of using Carbon 14 for dating including This problem is intended for instructional purposes only.
It provides an interesting and important example of mathematical modeling with an exponential function. The 1/13 ratio gets the correct answer of 21,203 years.
Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old.