weather conditions, social pressure, economic mismanagement, and radical agricultural changes
Irina handles money in a casino: Cashier
Stanley operates a ride at a theme park: amusement attendant
Michelle helps people exercise at a gym:Fitness Trainer
Jamie plays baseball on a nationally know team: Baseball Player?
Nguyen teaches are classes: Art teacher?
Honestly, I think the United States would eventually look the same as it does now. If they had not bought the land, they likely would have gone to war for it. It is very unlikely that they would have let it stay there as part of France or an independent country, both because of Manifest Destiny and for national security.
The only answer related to the subject is "the results of their experiments".
After Scientific revolution scientists came up with theoretical conceptions and tried to prove them with experiments. There had to be both theoretical explanation and emirical proof. Before they were much more liberal when it comes to coming up with "scientific theorems", which explained results of their experiments.