Human population after the $17$th century $A.D.$ is thought to be in which phase?

Exponential growth of a species can be expressed as:

Give scientific reasons: When a plant culture is grown in a limited amount of nutrient medium,growth is slow in the initial stage (lag phase). It increases rapidly in the exponential phase and again slows down in the stationary phase.

The formula of growth rate for population in a given time is

Maximum growth rate occurs in:

The given population growth curve represents the logistic growth curve. In this curve,identify what $A$,$B$,and $C$ indicate.