Radioactive dating involves determining which of the following? half-life decay index fossils depth of layers geologic time

The correct answer is half-life decay.  

A method of determining the age of a specimen of a mineral by finding the relative concentrations of certain radioactive elements present is known as radiometric dating or radioactive dating. In this age signifies the elapsed time from when the specimen of mineral was produced.  

The radioactive elements decay by half-lives, that is, if a half-life is equivalent to one year, then one half of the radioactive element will have decayed in the first year after the formation of mineral, and the other half will decay in the next year, and so on.