The formula, $\frac{\mathrm{dN}}{\mathrm{dt}}$ = rN represents

The formula, $\frac{\mathrm{dN}}{\mathrm{dt}}$ = rN represents exponential growth.

Resource (food and space) availability is essential for the unimpeded growth of a population. Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number. Then the population grows in an exponential or geometric fashion. If in a population of size N, the birth rates (not total number but per capita births) are represented as b and death rates (again, per capita death rates) as d, then the increase or
decrease in N during a unit time period t (dN/dt) will be
$\frac{\mathrm{dN}}{\mathrm{dt}}$ = (b – d) × N
Let (b–d) = r, then
$\frac{\mathrm{dN}}{\mathrm{dt}}$ = rN