The equation of Verhulst-Pearl logistic growth is $\frac{dN}{dt}=rN[\frac{K-<!--\; -\; -->N}{K}]$

From this equation, K indicates:

The Verhulst-Pearl logistic growth model is a mathematical model used to describe how a biological population grows when resources are limited.

The differential equation representing this growth is given by:
$\frac{dN}{dt}=rN\left[\frac{K-N}{K}\right]$

Let us break down the terms in this equation to understand their biological meanings:
1. N represents the population density at a given time t.
2. r represents the intrinsic rate of natural increase (also known as the biotic potential of the population).
3. K represents the maximum population size that a particular environment can support sustainably over time, given the available resources (such as food, water, and space). In ecology, this upper limit is called the carrying capacity.

The term
$\left[\frac{K-N}{K}\right]$
acts as a scaling factor representing the environmental resistance. When the population size (N) is very small compared to the carrying capacity (K), this fraction is close to 1, and the population grows exponentially. As N approaches K, the term goes to 0, causing the population growth rate (dN/dt) to slow down and eventually level off.

Therefore, the variable K specifically indicates the Carrying capacity.