Answer :
Final answer:
The rock sample is approximately 3.75 billion years old. This estimation is derived from understanding that Potassium-40 decays into Argon-40, and based on the ratio given, three half-lives have passed.
Explanation:
This question pertains to the radioactive decay of Potassium-40 into Argon-40 (Ar-40), which is a key concept in determining the age of rocks. In this context, having a ratio of one part Potassium-40 to three parts Argon-40 implies that three half-lives have passed because with each half-life, the quantity of Potassium-40 reduces by half while the volume of Argon-40 increases. The half-life of Potassium-40 is approximately 1.25 billion years, meaning this rock sample is roughly 3.75 billion years old.
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