An old asteroid is found. A rock from it yields 1.84 g of ^{238}U_{92} and 4.22 g of ^{206}Pb_{82}. The molar mass of ^{206}Pb_{82} is 205.974 g/mol, the molar mass of ^{238}U_{92} is 238.029 g/mol, and the half-life of ^{238}U_{92} is 4.46 x 10^{9} years.

How old is this asteroid? Express your answer with the appropriate units.