**Core Concept**
The demographic transition model describes the changes that occur in a population's birth and death rates as it develops from a pre-industrial to an industrialized society. The model consists of four stages, each representing a different population growth pattern.

**Why the Correct Answer is Right**
The late expanding stage is the third stage of the demographic transition model. During this stage, death rates continue to decline due to improvements in healthcare, sanitation, and living standards. However, birth rates remain high, leading to rapid population growth. This stage is characterized by a significant increase in population size, as the population grows exponentially. The late expanding stage is often seen in countries that have experienced significant economic growth and urbanization, but have not yet reached a stage of low fertility.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the early expanding stage is characterized by high birth and death rates, whereas the late expanding stage is marked by declining death rates and high birth rates.
**Option B:** This option is incorrect because the post-expanding stage is characterized by low birth and death rates, whereas the late expanding stage is marked by high birth rates and declining death rates.
**Option C:** This option is incorrect because the stationary stage is characterized by stable birth and death rates, whereas the late expanding stage is marked by rapid population growth.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the demographic transition model can be used to understand the changes that occur in a population's growth pattern over time. Understanding these changes can help policymakers develop strategies to address population-related issues such as poverty, healthcare, and education.

**Correct Answer: C. Late expanding stage indicates a significant increase in population size, characterized by declining death rates and high birth rates.**