Answer: 20.9 billion years.
Explanation: To estimate the age of the rock, we can use the fact that the half-life of uranium-238 is 4.47 billion years. This means that half of the uranium-238 in the rock would have decayed into lead-206 after 4.47 billion years, and half of what remains would decay in the next 4.47 billion years, and so on.
If 20% of the uranium-238 in the rock has decayed into lead-206, then 80% of the original uranium-238 is still present in the rock. This means that the rock has gone through one half-life of uranium-238 decay, and we can estimate its age by using the graph on page 253.
According to the graph, the ratio of lead-206 to uranium-238 after one half-life is approximately 0.027. This means that the rock contains 0.027 times as much uranium-238 as it did originally, and the remaining 80% of the uranium-238 corresponds to 0.8 times the original amount.
Therefore, we can estimate the original amount of uranium-238 in the rock as follows:
Original amount of uranium-238 = (0.8) / 0.027 = 29.63 times the current amount
Next, we can use the fact that each half-life corresponds to a reduction in the amount of uranium-238 by a factor of 2, to estimate the number of half-lives that have passed since the rock formed:
Number of half-lives = log2(29.63) = 4.88
Finally, we can estimate the age of the rock as follows:
Age of the rock = (4.88) x (4.47 billion years per half-life) = 20.9 billion years
Therefore, we can estimate that the age of the rock is approximately 20.9 billion years.