My 93 year old dad does both physical and mental exercise. His feet have started giving him problems with support, so he's been walking with a cane or even walker for aerobic exercise just because he's afraid of falling down, but he does stretching and situps and stuff all the time, and though he is limited in the food he can eat now, he eats as healthy as his diet will allow.
To me, most importantly, is that he constantly exercises his mind. For the past several years, he has started the encyclopedias at "A", read through to "Z", then started over again. I've been in the habit for the last year of also sending him easy to read books on various history topics, which is an interest of his. Further, he sits down at least a few times a week and does math problems to, as he says, "keep his brain goin'. "
I am 100% certain it all has made a difference and warded off dementia.