Final answer:
A population reaches a stable-age distribution when the proportion of individuals in each age group remains the same, which typically happens during Stage 4 of the Demographic Transition Model when birth rates equal death rates and the population has reached its carrying capacity.
Step-by-step explanation:
A population reaches a stable-age distribution when the proportion of individuals in each age group remains the same over time. This typically occurs during the later stages of the Demographic Transition Model (DTM), after a society has passed through periods of high birth and death rates (Stage 1) and arrives at a point where both the birth rate and death rate are low (Stage 4). At this point, the birth rate drops to match the death rate, leading to zero population growth, and the population stabilizes with little or no long-term change in total numbers. When this equilibrium is reached, the population has leveled off at its carrying capacity, meaning the environment supports the maximum number of individuals without degradation of habitat or resources.