Problem

Uranium ores on the earth at the present time typically have a composition consisting of 99.3% of the isotope

{}^{238}_{92}\mathrm{U}

and 0.7% of the isotope

{}^{235}_{92}\mathrm{U}

. The half-lives of these isotopes are

4.47 \times 10^9

yr and

7.04 \times 10^8

yr, respectively. If these isotopes were equally abundant when the earth was formed, estimate the age of the earth.