Sigmoid growth, also known as S-shaped growth, describes a pattern where population density initially increases slowly, then rapidly (exponentially), and finally slows down and stabilizes as resources become limited, forming an S-shaped curve when plotted over time. 

When a population doubles in a consistent timeframe, it strongly suggests exponential growth, meaning the population is increasing at a rate proportional to its current size. Exponential growth occurs when a quantity (like a population) increases by a constant percentage or factor over equal time intervals. 

A population explosion refers to a rapid increase in the number of organisms in a specific area, often exceeding the ability of the environment and economy to sustain them. 

Rapid growth" refers to a situation where a population increases or develops at a very fast rate, often unexpectedly.