  Carey's Equality pertaining to stationary models is well known. In this
paper, we have stated and proved a fundamental theorem related to the formation
of this Equality. This theorem will provide an in-depth understanding of the
role of each captive subject, and their corresponding follow-up duration in a
stationary population. We have demonstrated a numerical example of a captive
cohort and the survival pattern of medfly populations. These results can be
adopted to understand age-structure and aging process in stationary and
non-stationary population population models. Key words: Captive cohort, life
expectancy, symmetric patterns.
