Asymptote in a logistic growth curve is obtained when

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

Consider a population of $10$ million cells. Given the per-capita birth rate of $0.002$ (per unit time) and the per-capita death rate of $0.002$ (per unit time), the expected number of cells after $10$ generations is

Exponential growth cannot be sustained for a long time due to:
$I.$ Limited space and nutrients
$II.$ Accumulation of toxic agents
$III.$ Unlimited space and nutrients
$IV.$ Accumulation of nutrient agents
Choose the correct combination of options:

If a population adds $20$ new individuals per year and the total population after $2$ years is $75$,what was the initial population size?

When environmental conditions are favourable,then the population growth curve will be