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It is assumed the world's population first reached 1 billion in 1804 and 2 billion in 1927. If growth was constantly exponential through that period - an assumption that ignores the disaster of the First World War and the flu epidemic of 1918 - the estimate in 1812 would be 1,050,000,000. Given that the years 1804 to 1812 were in the middle of the Napoleonic era, it's unlikely the number is more than a few million above the quoted estimate.

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Q: How many people lived in the U.S. in 1812?
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