A large nuclear power plant has a rated capacity of \(1 \mathrm{GW}\) electric. Its actual output is estimated to average about \(80 \%\) of capacity due to the need for maintenance and imperfect match between supply and demand. Assuming that year-round average residential electricity needs are about \(1 \mathrm{~kW}\) electric per housing unit and there are three residents per unit, estimate how many power plants would be needed to satisfy the demand of a metropolitan area with a population of 30 million.