Final answer:
The field of medicine was considered a well-respected profession by the 1800s. This is contextualized by the founding of the American Medical Association in 1847, despite the discrimination Black physicians endured at the time.
Step-by-step explanation:
The field of medicine has been considered a respectable and prestigious profession for many centuries, however, the level of prestige and respect specifically in the context of professional organizations like the American Medical Association (AMA), which was founded in 1847, suggests that by the 1800s medicine was already on its way to being a well-respected profession. Despite this prestige, the profession has not been without its challenges and biases, particularly toward Black physicians and nurses. Barriers such as refusal of membership in the AMA, and segregation in hospitals, were prevalent during the late nineteenth and early twentieth centuries. Over time, events and societal changes such as the formation of the National Medical Association in 1895 and subsequent reforms in medical education and practice have contributed to the ongoing development and increase in prestige of the medical profession.
In accordance with history and the information provided, the most accurate answer to the multiple-choice question is B) 1800, recognizing that while respect and prestige for the medical profession may have increased since then, its status as a respected field was already established by the 19th century.