When any population reaches the carrying capacity there might be chance of cathostrophic population check which decreases the rate of increase of population by killing large number of population.....
cathostrophic population check means sudden decrease in population by environmental factors like earthquake, volcanic eruption ,natural disaster or disease etc...
the live example of cathostrophic population check is the disease called Corona by COVID-19 which suddenly affect the human population as Earth carrying capacity for human population is 8 billion and owr population almost reach up to 7.4 billion

Introduction:
The sigmoidal growth curve, also known as the S-shaped curve, is a common representation of population growth. It describes the pattern of population growth over time, starting with slow growth, followed by a rapid increase, and then a gradual leveling off as the population approaches the carrying capacity of the environment.

Explanation:
As the number of individuals approaches the carrying capacity of a population, several predictions can be made based on the sigmoidal growth curve:

1. Population biomass will remain the same:
The carrying capacity represents the maximum number of individuals that the environment can sustainably support. As the population reaches this capacity, the available resources become limited. Therefore, the population biomass, which refers to the total mass of all individuals in the population, is expected to remain relatively constant.

2. Population density will increase exponentially:
Population density is the number of individuals per unit area. As the population approaches the carrying capacity, the available space becomes limited. This leads to increased competition for resources and territorial disputes among individuals. Consequently, the population density is expected to increase exponentially as individuals try to occupy the available space.

3. Population growth rate will decrease:
The growth rate of a population is the rate at which the number of individuals in the population changes over time. Initially, the population growth rate is high when resources are abundant and competition is low. However, as the population approaches the carrying capacity, the growth rate starts to decline. This is because the available resources become limited, leading to increased competition and decreased reproductive success. As a result, the population growth rate decreases.

Conclusion:
In summary, the sigmoidal growth curve predicts that as the number of individuals approaches the carrying capacity of a population, the population biomass remains the same, the population density increases exponentially, and the population growth rate decreases. These predictions are based on the principles of limited resources, increased competition, and the concept of carrying capacity.