New research documents another decline in dementia rates, but experts say the rising numbers of older Americans may halt that trend unless better ways are found to keep brains healthy.

The study shows the rate of Alzheimer’s disease and other dementias in people 65 and older dropped to about 9 percent in 2012 from nearly 12 percent in 2000, continuing a decline noted in earlier research.

Older adults with the most schooling had the lowest dementia rates, and the average education level increased during the study years.

Led by University of Michigan researchers, the study was published in JAMA Internal Medicine. The National Institute on Aging paid for the research.

Researchers analyzed nationally representative government surveys of about 10,500 older adults in both years, including some living in nursing homes. They were interviewed and given mental tests by phone or in person; spouses or relatives responded for those impaired by dementia or other illness.

The dementia rate declined amid a rise in diabetes and heart disease. Both of these ailments increase risks for Alzheimer’s and other dementias, but the researchers say better treatment for the diseases may explain the improved results.

Obesity rates also increased, while dementia was most common among underweight adults. Previous research has shown weight loss may precede dementia by several years and that late-life obesity may be healthier than being underweight. But a journal editorial says more research is needed to determine whether excess pounds in older age somehow protect the brain.

Dementia was most common in the oldest adults: In 2012, almost 30 percent of people 85 and older were afflicted, vs. just 3 percent of those 65 to 74.

The number of adults 85 and older is rapidly rising and is expected to triple by midcentury. John Haaga, director of the National Institute on Aging’s behavior and social research division, said dementia rates would have to decline much more sharply than they have to counteract that trend.

The Alzheimer’s Association estimates that about 5 million people 65 and older have Alzheimer’s, and that is expected to rise to almost 14 million by 2050.

The average education level climbed during the study. About 45 percent of older adults had at least 13 years of education in 2012, vs. about 33 percent in 2000.

Previous studies have found less dementia in highly educated people, but it isn’t known whether education is somehow protective or whether it helps people compensate for brain changes linked with Alzheimer’s and other dementias.

Studies on brain-training exercises have had conflicting results.

Haaga said more research is needed to explain the education-dementia link and to explore potential treatments that mimic the effects of education to stave off dementia.

Meanwhile, experts say there are ways to help keep your brain healthy. Those steps include avoiding smoking, eating healthy foods and getting plenty of exercise. Experts also advise staying mentally active: Take a class, learn a new skill or hobby.

“There is reason to hope that you’re not doomed if you didn’t get massive education early in life,” Haaga said.