Final answer:
To obtain the numerical age of a rock or fossil, geologists use radiometric dating techniques that rely on known radioactive decay rates of isotopes. These techniques allow calculations based on the ratio of parent to daughter atoms, providing an estimate of how many half-lives have passed since the rock or mineral formed.
Step-by-step explanation:
The method used to obtain the relative age of a rock or fossil would be b. Original horizontality. However, if we are discussing methods to obtain the numerical or absolute age of a rock or fossil, we would refer to radiometric dating techniques. These techniques involve the use of radioactive isotope systems to determine quantitative ages for rocks, minerals, and some fossils.
Geologists can determine how many half-lives have passed for an isotope system by analyzing the ratio of parent and daughter atoms within the geologic material. Radioactive decay rates are known and stable, allowing geologists to estimate ages with assumptions that, initially, no daughter atoms were present and the system remained closed. In cases where these assumptions do not hold, geologists have developed methods to correct potential inaccuracies.
Absolute dating methods are contrasted with relative dating methods, which only establish the sequence of events without numerical ages. By understanding the rate at which radioactive isotopes decay, scientists can calculate the time elapsed since the rock or mineral formed, thereby determining its age.