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Q:  

I am examining the relationship between metropolitan-level foreclosure and racial residential segregation in U.S. American cities between 1990 and 2010.

I am including characteristics which can be found in decennial census surveys and ACS estimates. One variable absent from these sources is the age in which the largest city in the metro reached a population size of 50,000.

I was curious to know of any source that has already compiled this.

A:  

Assuming your current metro areas are relatively large, this source by Campbell Gibson from the Census Bureau should cover most of your needs:

Population of the 100 Largest Cities and Urban Places: 1790 to 1990

This document provides data on a decade by decade basis rather than for places x year so you'll have to compile the data yourself so that you can look to see which decade Detroit, Pittsburgh, San Antonio, etc. reached 50,000.

I suspect this will meet your needs but one other source is a study out of ICPSR:

ICPSR #2896:Historical, Demographic, Economic and Social Data: US 1790-2002

Parts 58-69 consist of data from City data books for 1944, 1948, 1952, 1956, 1962, 1967, 1972, 1977, 1983, 1988, 1994, and 2000.  One of the data points is population.

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