What is the correct mathematical representation of the Verhulst-Pearl logistic growth equation?

The population of an insect species shows an explosive increase in numbers during the rainy season,followed by its disappearance at the end of the season. What does this show?

Biotic potential is:

The formula for exponential population growth is

$I.$ Populations evolve to maximize their reproductive fitness,also called Darwinian reproductive fitness (higher $r$ value),in the habitat in which they live.
$II.$ The population growth rate $r$ is inversely related to generation time.
$III.$ The housefly,which has a short life span and produces a large number of eggs,could be considered as a '$K$' selected species.
$IV.$ Under a particular set of selection pressures,organisms evolve towards the most efficient reproductive strategies.
$V.$ Life history traits of organisms have evolved in relation to the constraints imposed by biotic and abiotic factors in their habitat.
Select the combination of correct statements.

The integral form of the exponential growth equation is $N_{t} = N_{0} e^{rt}$. Identify $A, B, C$,and $D$ from the given equation where:
$A$: Population density after time $t$
$B$: Population density at time zero
$C$: Intrinsic rate of natural increase
$D$: The base of natural logarithms $(2.71828)$