Which is not true for $J-$shaped growth curve?

With the help of suitable diagram describe the logistic population growth curve.

Which of the following is correct

$I.$ In a population, birth rate and death rate refer to per capita births and death respectively

$II.$ In nature, we rarely find isolated single individuals of any species

$III.$ The size of population for any species is stable phenomena

$IV.$ Ecological effects of any factors on a population growth are generally reflected in its size/population density

Change in population size equation with prolonged exponential phase can be converted into logistic growth equation by multiplying it with