The natural uranium/lead "clock" technique can be used to estimate the age of rocks. Assume that, at the time of solidification from the molten state, a rock contained the radioactive isotope uranium-238. U-238 decays to a stable end product, lead-206, through a series of disintegrations. This decay is known to have a half-life of 4.5 x 10^9 years. Each uranium atom that decays eventually results in the formation of one lead atom. Assuming that the rock did not contain any lead-206 atoms originally, find the age of the rock when the ratio of uranium to lead atoms is 8 to 1.