The demographic transition model shows population change over time through 5 stages. In Stage 2, the population begins to grow as the death rate falls due to improved healthcare, but the birth rate remains high. Countries in Stage 3 experience rapid population growth as the birth rate also starts to decline due to factors like family planning and changing social norms, while the death rate continues falling. Stage 4 is when population growth levels off as both birth and death rates stabilize at low levels in developed nations.