Why did the Virginia Company establish the colony at Jamestown?

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Britain came in somewhat late to the game as far as imperialism in the Americas. Beginning with Columbus' journey to Hispaniola, Spain and Portugal had been colonizing the parts of America with tropical weather. These areas were perfect for growing valuable crops like sugar cane, cacao, and indigo (a dye). Spain also benefitted by pillaging the Incan and Aztec empires, and mined tons of silver.

Other imperial powers had to involve themselves in piracy for a portion of the Spanish wealth. French, British, and Dutch ships all participated in government sponsored piracy. France was the next to find good income by settling the far north (present-day Quebec) and trading with Native Americans for valuable fur. The Dutch then set up fur trade a bit further south in present day New York.

By the time the British Empire was ready to begin colonizing, the space they could colonize in was pretty limited - Spain controlled Florida and most of the land to the South, and the French fur trading colonies controlled anything north of Nova Scotia.

The land around the Chesapeake Bay (where Jamestown would be settled) did not have the weather to grow sugar or indigo, and was not cold enough to supply good furs. Instead, the Virginia Company got investors to hope that there would be gold or silver on the land. The workers who founded Jamestown were sent to find a way to make the colony profitable, and early on mostly searched for valuable metals.

There weren't any, so Jamestown very nearly failed for almost a decade. Soon, the discovery of tobacco as a valuable crop that grew in the region made Jamestown into a profitable colony.