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 4.5x10^9 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.