Final answer:
The age of a rock with equal concentrations of lead-206 and uranium-238 is 4.5 billion years, which corresponds to one half-life of uranium-238.
Step-by-step explanation:
The question is about determining the age of a rock by using ratios of lead-206 (Pb-206) and uranium-238 (U-238) and the concept of half-life in radioactive dating. Since the half-life of U-238, which decays to Pb-206, is 4.5 billion years, after one half-life, the amount of U-238 would be equal to the amount of Pb-206 in a sample. If a rock has an equal concentration of Pb-206 and U-238, it indicates that one half-life period has elapsed, and therefore, the rock is 4.5 billion years old.