What would be the mathmatical equation to explain dog exercise? (see details)

While wandering about Manhattan I saw several dog walkers. Many had multiple dogs of all sizes from Great Dane to Maltese. The little dogs were practically running as the large dogs sauntered along. I have two questions. One is what mathmatical equation would reveal the increase of energy expelled by the little dog vs the big one. Secondly- could the reason smaller dogs on average live longer than larger dogs be attributed to the increased exercise?