In humans, the basal energy metabolism is thought to decline linearly with age. On the other hand, in the nematode Caenorhabditis elegans, two research groups reported independently that it declined exponentially. In this study, furthermore, we used various lifespan-mutant strains to determine whether the previous conclusion is more likely to be true. We can indirectly estimate the metabolic energy by conveniently measuring the oxygen consumption rates of C. elegans using an optical apparatus. From the profile of respiratory rates as a function of age, we can quantitatively isolate the physiological decline rate, lambda, that exponentially represents the decay rate of respiratory activity with age. In addition, quantitative analysis indicates that the respiratory activity of worms has a finite value in advanced age. We also show that the maximum and mean lifespans strongly correlate with the reciprocal of the lambda. These findings offer crucial biochemical evidence for a molecular mechanism at work in biological aging. Consequently, we here propose a mechanism based on a chemical reaction and offer a definition of the physiological decline rate and the finiteness of respiratory activity in advanced age.