The given figure illustrates the growth curve of a population in a...

The given figure represents a logistic growth curve, which is described by the Verhulst-Pearl Logistic Growth equation:

$\dfrac{dN}{dt} = rN \left(\dfrac{K-N}{K}\right)$

where:
$N$ = Population density at time $t$
$r$ = Intrinsic rate of natural increase
$K$ = Carrying capacity

At point 'P' on the curve, the population has reached its carrying capacity, meaning $N \approx K$.

Substituting $N = K$ into the term \left(\dfrac{K-N}{K}\right)$, we get:<br>\left(\dfrac{K-K}{K}\right) = 0$

As the value of \left(\dfrac{K-N}{K}\right)$approaches zero, the population growth rate \left(\dfrac{dN}{dt}\right)$ also approaches zero. This indicates that the population size has stabilized and is no longer growing.

Answer: The value of $\left(\dfrac{K-N}{K}\right)$ approaches zero, causing the population growth rate \left(\dfrac{dN}{dt}\right)$ to approach zero.