Population Data from US Census

UsaPopList= { {1800,5308483}, {1810, 7239881}, {1820,9638453},{1830, 12866020}, {1840, 17069453}, {1850,  23191876}, {1860, 31443321 }, {1870,  38558371}, {1880, 50189209 }, { 1890, 62979766 }, {1900,  76212168}, {1910,  92228496}, {1920,  106021537}, {1930,  123202624}, {1940, 132164569 }, {1950,  151325789}, {1960,  179323175}, {1970,  203302031}, {1980,  226542199}, {1990, 248709873 }, {2000,281421906  }, {2010, 307745538} }

ListPlot[UsaPopList]

M2=Fit[UsaPopList,{Exp[t],1},t]

M3=Fit[UsaPopList,{Exp[t-1800],1},t]