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She, being a faithful Christian, told me to write what the textbooks stated for the sake of the exam without arguing. I had the same thought about the circular reasoning involved in estimating the age of the earth, and even told my teacher that it sounded absurd.
This standard content of C14 can then be used for wood not associated with a historically documented date.(They conveniently forget to mention that the tree ring chronology was arranged by C14 dating.The scientists who were trying to build the chronology found the tree rings so ambiguous that they could not decide which rings matched which (using the bristlecone pine).In fact, 14C is forming FASTER than the observed decay rate.This skews the 'real' answer to a much younger age.