Final answer:
The historical boomtown Pithole City experienced rapid population growth and decline within 20 years, reaching about 10,000 at the peak, making the statement true.
Step-by-step explanation:
The question about Pithole City's rapid population growth and decline appears to be a historical one, rather than a purely mathematical, scientific, or literary problem. This narrative of growth reflects patterns seen in real historical boomtowns associated with economic phenomena like gold rushes or oil booms. Pithole City, also known as Pithole or Pithole Creek, is a real historical example of a boomtown that grew in the context of the Pennsylvania oil rush in the 1860s. At its peak, it did indeed reach a population of around 10,000 before declining to zero as the oil rush subsided.
Such dramatic changes in population figures are part of the broader social studies field, which examines how societies change over time. Regarding boomtowns, the factors influencing such growth and decline typically stem from economic opportunities that prompt a rapid influx of people, followed by a decline when those opportunities no longer exist. Historically, the case of Pithole City is a classic example that confirms the true or false statement in the question as 'true'.