Explain how old is the rock

Question

A rock was recently discovered near the Arctic Circle which was found to contain 1.0103nanograms (ng) of  ²⁰⁶Pb and 5.5732 ng of²³⁸U. The decay series of ²³⁸U to²⁰⁶Pb is a process which has a half-life of 4.5x10⁹ years. We assume the first step in this decay series is, by far, the slowest and that all the ²⁰⁶Pb found in the sample is derived from this decay process. Discuss how old is the rock?

1 amu = 1.6606x10^-27 kg1 J = 1 kg•m²s^-2c = 3.000x10⁸m/sN_A = 6.022x10²³mass of proton = 1.00728 amu mass of neutron = 1.00867 amu mass o f electron = 0.0005486 amu