Answer:
The answer to the question: Which future states grew dramatically in the late 1700´s and early 1800´s, would be, that it was the future states of Louisiana, Alabama, Mississippi, but most of all Florida, which grew dramatically from the influx of new settlers, in this gap period.
Explanation:
According to historical data, and research, although most people tend to think that the biggest movement of new settlers in the U.S, during its colonial period, was towards the West, the information shows that during the periods between the 1700´s and 1800´s, most white settlers went southwards, towards the territories that would later become the states of Louisiana, Alabama, Mississippi, and most importantly, Florida, more than westwards.