Final answer:
The first successful Barbadian expedition and settlement in North America was at Charles Town, where colonists applied their plantation and slavery experience from sugar cane agriculture to the new Carolina colony in 1669.
Step-by-step explanation:
The first successful expedition and settlement by colonists from Barbados in North America was at Charles Town. In 1669, these settlers left Barbados due to limited land opportunities and ventured to the new Carolina colony. With their expertise in colony-building and the use of slavery to address labor shortages, similar to their practices in the sugar plantations of the Caribbean, they founded a settlement at the confluence of the Ashley and Cooper Rivers on the South Carolina coast. This new settlement, Charles Town, would become profoundly influenced by the Barbadian model and eventually lead to the widespread use of enslaved labor in agriculture across the southern English colonies.