Final answer:
The growth of the American colonial population from around 250,000 in 1700 to over 2,000,000 by 1770 was caused by natural increase and significant levels of immigration from Europe.
Step-by-step explanation:
During the period 1700 to 1770, the American colonial population saw significant growth mainly due to both natural increase and immigration. The death rates among colonists fell while the birth rates remained high. This scenario contributed to the rapid population growth. Moreover, the colonies also experienced substantial immigration, which not only increased the population numbers but also the cultural diversity within the American colonies. This immigration included a wide range of European settlers and indentured servants, as well as an increase in the importation of African slaves, although this latter point was less significant in the northern colonies.
It is important to note that most new settlers to the American colonies during this period came as family units, which made the colonies self-sustaining more quickly than if they had come individually. The combination of longer life expectancies, which approached that of settlers in the northern colonies, and a steady flow of immigrants contributed to the considerable demographic change.