# Can I get an x-value for a given y-value using an interpolation function? [duplicate]

I'm brand new to Mathematica and struggling figure this all out.

I made an interpolating function with the following (year, population) data. I'm trying to figure out what year the population reached certain amounts. I've Feel like I've tried just about everything except the right thing. I would appreciate any help.

PopData = {{1790, 3929214}, {1800, 5536631}, {1810, 7239881}, {1820, 9638453}, {1830, 12866020}, {1840, 17069453}, {1850, 23191876}, {1860, 31443321}, {1870, 38558371}, {1880, 49371340}, {1890, 62979766}, {1900, 76212168}, {1910, 92228496}, {1920, 106021537}, {1930, 123202624}, {1940, 132164569}, {1950, 151325798}, {1960, 179323175}, {1970, 203211926}, {1980, 226545805}, {1990, 248709873}, {2000, 281421906}, {2010, 309162581}, {2020, 331449281}};

ListPlot[PopData, PlotStyle -> Directive[Red, PointSize[0.02]], AxesLabel -> {Year, U . S . Population}, LabelStyle -> Directive[Black, Bold]]popfxn = Interpolation[PopData]

Plot[popfxn[x], {x, 1790, 2020}, AxesLabel -> {Year, U . S . Population}, LabelStyle -> Directive[Black, Bold]]

Show[ListPlot[PopData, PlotStyle -> Directive[Red, PointSize[0.02]]], Plot[popfxn[x], {x, 1790, 2020}], AxesLabel -> {Year, U . S . Population}, LabelStyle -> Directive[Black, Bold]]

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• You need to solve the equation popfxn[x]==pop0, try NSolve. Oct 15 at 8:51
• This question has answers here and here Oct 15 at 8:52

dat = {{1790, 3929214}, {1800, 5536631}, {1810, 7239881}, {1820,