The half$-$life for the radioactive decay of U$-238$ is $4\mathrm{.}5$ billion years and is independent of the initial concentration. How long will it take for $20\%$ of the U$-238$ atoms in a sample of U$-238$ to decay? If a sample of U$-238$ initially contained atoms when the universe was formed $13\mathrm{.}8$ billion years ago, how many U$-238$ atoms does it contain today?