Final answer:
The provided information does not specifically detail trends in prostitution to determine when it experienced a sharp increase or peaked. Economic conditions like unemployment rates and legal factors can impact prostitution trends.
Step-by-step explanation:
The specific data points provided do not outline the history of prostitution in a way that allows for a precise answer to when prostitution experienced a sharp increase or when it peaked. However, it is known that prostitution, both formal and informal, was common in nineteenth-century cities and has fluctuated due to various factors such as economic conditions, which could be inferred from data like the U.S. Unemployment Rate. Societal factors and the legal environment, such as the law on prostitutes, also significantly impact such trends. While the provided information refers to unemployment data and population age distribution from select years and periods, it does not directly relate to the prevalence or changes in prostitution rates during those times. Historical studies on prostitution often require comprehensive analysis beyond simple datasets, including legislative changes, social attitudes, and economic shifts.