Find the correct mathematical expression for geometric growth resulting in a J-shaped population growth curve.

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 

dN/dt = (b – d) × N 

Let (b–d) = r, 

then dN/dt = rN

The r in this equation is called the ‘intrinsic rate of natural increase’