Final answer:
The assertion is false; during the eighteenth century, most British colonists in North America lived in rural areas and the substantial urban growth occurred later in the mid-nineteenth century.
Step-by-step explanation:
The statement that by the eighteenth century, nearly fifty percent of British colonists in mainland North America lived in a city is false. In the 1700s, most British colonists in North America were not urban dwellers; rather, they were largely self-sufficient and lived in rural areas. It was not until the mid-nineteenth century that the urban population began to increase significantly due to industrialization and the consequent demand for labor.
This urban growth was reflected to a greater extent in Great Britain itself, and the colonial American cities like Philadelphia, Boston, and New York did not experience a substantial urban growth until a century later. Therefore, the urbanization of the British American colonies did not reach a point where half the population lived in cities during the eighteenth century.