How do knowing the half-life of carbon 14 can tell scientists the absolute age of a rock sample

Carbon 14 dating makes some assumptions that are not exactly true, but likely close enough for most purposes. 1 that the ratio of carbon 13 to carbon 14 in Earth's atmosphere has not changed over the last million years. 2 that living things give zero preference to carbon 13 over carbon 14.
3 Carbon 14 dating is often unreliable for rocks which have low carbon content, such as quartz, and some other assumptions.

the answer is true.

this statement is true.