The formation, accretion and growth of supermassive black holes in the early universe are investigated. The accretion rate ${dot M}$ is calculated using the Bondi accretion rate onto black holes. Starting with initial seed black holes with masses $M_{rm BH}sim 10^2-10^3M_{odot}$, the Bondi accretion rate can evolve into a supermassive black hole with masses $M_{rm BH}sim 10^9-10^{10}M_{odot}$ and with a young quasar lifetime $sim 10^5-10^6$ years by super-Eddington accretion.
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