On The Oregon Trail: American Settler, for Android, do trees eventually grow back after you've chopped them down?
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I found this link which has some interesting information on this issue.
The generally gist seems to be that you need to keep the game running in the foreground for either saplings and/or partial tress to regrow. The rate is claimed to be around 1/7 per hour.
Personally this does seem like a bug to me, but I guess you also have to consider the fact that is take 7 energy to remove a tree. If the grow back while you were offline, this might prove time consuming just to clear a small area a trees when you consider the energy cap (especially so soon in the game)... then again, if you plant a sapling you clearly want a tree to grow there anyway.
Bad design or a bug? I guess time will tell