There are a number of Eick families in Michigan in 1900, 1910 and 1920.
The most likely one appears to be Charles Eick who apparently immigrated in 1890.
In 1900 he was in Macomb County, Sterling Twp.
Charles Eick, age 50, born May 1849 in Germany.Unfortunately the writing on this census page is very difficult to read, so I can't tell when he immigrated. He appears to have been a farmer.
Wife was Ida F. - they hadbeen married one year. She had had two children, both were still living.
The family included: Richard, age 13, born in Russia Mary, age 8, born in Michigan Ida (last name looks like Trienst), stepdaughter,age 5, born in Germany. Walter (last name looks like Sietz), born in Michigan, 1 years old, step-son
On the same census page, living in another household as a laborer was 16 year old Edward Eick, born in Russia
I didn't find either Charles or Edward in 1910, but I did find Charles in 1920, living in 10th ward Detroit, Wayne County.
Charles, age 70, working as a janitor in a factory. Strangely, he is shown as married, but the next 3 are his children, then Ida Eick is listed as a lodger, who is married, age 53. Walter, age 21, born Michigan Martha, age 16, born Michigan Emma, age 14, born Michigan
Charles had immigrated in 1890, Ida in 1895.
If these aren't the correct Eicks, please provide more information to help find them in the census. (dates of birth, places they lived, etc.)BTW - There weren't any Eick families in Genesee County in 1900 - 1920.