The following data represent the U.S. population from 1790 to 2010. Find a dynamical system model that fits the data fairly well. Test your model by plotting the predictions of the model against the data.

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Year Population 1790 3,929,000 1800 5,308,000 7,240,000 1810 1820 9,638,000 1830 12,866,000 1840 17,069,000 1850 23,192,000 1860 31,443,000 Year Population 1870 38,558,000 50,156,000 1880 1890 62,948,000 1900 75,995,000 1910 91,972,000 1920 105,711,000 1930 122,755,000 1940 131,669,000 Year Population 1950 150,697,000 1960 179,323,000 1970 203,212,000 1980 226,505,000 248,710,000 281,416,000 308,746,000 1990 2000 2010