Final answer:
Nursing homes are not growing as rapidly as other forms of long-term care like assisted living, adult family homes, and home health care due to shifts in demographic trends, costs, and the balance of care needed.
Step-by-step explanation:
Among the options provided for long-term care of frail elders, nursing homes have not been growing as rapidly as the other options. With the shift in demographic trends and family dynamics, along with costs considerations, the popularity of nursing homes is not increasing to the same extent as assisted living, adult family homes, and home health care. These other options often provide a more appealing balance between independence, affordability, and the level of care needed. Assisted living and adult family homes offer a community setting with varying levels of support, and home health care allows elders to remain in the familiarity of their home with the assistance of healthcare services.