Let me do something easier. According to the Census, in 2000 the black population of the Detroit-Warren-Livonia MSA was just over 1 million [[1,012,262) In 2010 the black population of the same Census MSA was 1,017,405. Wherever the blacks who left the city went, there wasn't any significant net out-migration of blacks from the metro area. Since I doubt there was a lot of in-migration, almost all of those people had to be relocating within the metro area.
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