According to one cosmological theory, when uranium was first generated in the early evolution of the universe following the “big bang,” the isotopes ²³⁵U and ²³⁸U were produced in equal amounts. Given the half-lives of 4.51 x   10⁹ years for ²³⁸U and 7.10  x 10⁸ years for ²³⁵U, calculate the length of time required to reach the present distribution of 137.7 atoms of ²³⁸U for each atom of ²³⁵U.