"In 1827, Gen. Wm. Clark purchased 37,000 acres of land, including the site on which Paducah now stands, for $5".
What the sign forgot to tell you is that Clark purchased the deed to the land directly from the United States Government, not from the people who actually owned and occupied the land, who were forced out. Oops.
The city was called Pekin then, by the Native Americans and white settlers who lived together in an unusual-for-then arrangement of harmony and cooperation, until Clark showed up, claimed to have bought the land for a five-spot, and told everyone they had to scram.
The Indian Chief Paduke, who ran Pekin, could have fought Clark over the land, but was smart enough to realize that most likely, he would be wiped out (along with everyone else) by the U.S. Army who would come in as Clark's backup if needed to enforce the land transfer. So, Paduke and everyone else in Pekin peacefully moved along to Mississippi. As a gesture of thanks for being so cooperative and docile, Clark named the city after the Chief but got his name wrong. What a sport.