Answer:
The reason why there was a big population increase in the colonies between 1700 and 1776, is: immigration, especially of large family groups, from Europe towards the Americas.
Step-by-step explanation:
There have been many factors used to explain why people decided to emigrate from Europe into the newly established American colonies, but probably two of the strongest ones were: religious persecution and conflict between nations in the old continent. In fact, it is possible to say that these two causes led great numbers of people, but most importantly, large family groups, to leave their native lands to re-settle in the American lands. But this was most notable between the periods of 1700 and 1776.