If in a population of size $N$,the birth rates are represented as $b$ and death rates as $d$,then the increase or decrease in $N$ during a unit time period $t$ will be:

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

Maximum growth rate occurs in:

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 above graph indicates . . . . . . with relation to population.

State the popular humorous anecdote about the dramatic demonstration of how a large population can build up exponentially.