Which of the following is correct for $r$-selected species?

If the population density at time $t$ is $N_t$,then the population density at time $t+1$ is given by:

Read the following statements and determine how many of them are correct:
$(1)$ Population is the total number of individuals of a species in a given area at a given time.
$(2)$ Developed countries show a low birth rate.
$(3)$ An equal proportion of reproductive and post-reproductive age individuals indicates a stable population.
$(4)$ In the presence of limited resources,the growth curve is sigmoid ($S$-shaped).

The statement 'Food supply increases in an arithmetic progression,while population tends to increase in a geometric progression' was proposed by:

The number of deaths and births in the last stage of the plateau growth curve of a population will be:

Which one of the following is $INCORRECT$ about the logistic growth model?