Diane, my JENKIN family lived in Eureka from 1888-1900. Here's what I found in the online Utah encyclopedia:
Eureka is located approximately seventy miles southwest of Salt Lake City in Juab County. Incorporated as a city in 1892, Eureka became the financial center for the Tintic Mining District, a wealthy gold and silver mining area in Utah and Juab counties. The district was organized in 1869 and by 1899 became one of the top mineral producing areas in Utah. Eureka housed the "Big Four" mines -- Bullion Beck and Champion, Centennial Eureka, Eureka Hill, and Gemini-and later the Chief Consolidated Mining Company.
As with other mining towns, Eureka developed from a camp to a settlement then town. It benefited from competing transportation services of the Union Pacific (1889) and the Denver and Rio Grande Western (1891) railroads. Census statistics indicate the following population figures through 1930, when the impact of the Depression changed its fortunes: 1880 - 122; 1890 - 1,733; 1900 - 3,325; 1910 - 3,829; 1920 - 3,908; 1930 - 3,216. That Eureka's population exhibited ebbs and flows between census years was attributed to the transitory character of a mining town. By the 1980s the population fell below 700.