rN

Without environmental resistance ((K - N)/K), the population would grow exponentially at a rate equal to rN, an unrealistic expectation for any extended period of time, although it could occur for a short time when the population (N) is very small.

Competitive exclusion principle 2008

Mathematically, the exponential model is: dN/dt = rN

Exponential growth 2008

One simple version of the logistic model is expressed in the equation dN/dt = rN ((K - N)/K).

Competitive exclusion principle 2008

Under those conditions (K – N)/K approaches one and dN/dt approaches rN.

Competitive exclusion principle 2008

Could two different potentials, v1 (r) and v2 (r), with associated different groundstates 1 (r1, ..., rN) and

Walter Kohn - Autobiography 1999

Then the probability amplitude of the system is a function of the N variables r1, r2, ..., rN, and in addition, of the time t to which the amplitude is referred.

Sin-Itiro Tomonaga - Nobel Lecture 1972

Namely, while one could calculate the probability of finding particles at points with coordinates r1, r2, ..., rN, all at the time

Sin-Itiro Tomonaga - Nobel Lecture 1972

On the other hand, in Dirac's theory which does not use the Hamiltonian formalism, it becomes possible to consider different time variables for each particle, so that the probability amplitude can be expressed as a function of r1, t1, r2 t2, ..., rN tN.

Sin-Itiro Tomonaga - Nobel Lecture 1972

Now, as an example, let us consider a system composed of N particles, and let the coordinates of each particle be r1, r2, ..., rN.

Sin-Itiro Tomonaga - Nobel Lecture 1972

Yes, population growth is slowing, but your link clearly shows via the differential dN by dt = rN a roughly exponential growth and any mitigation is a long way off.

Army Rumour Service 2009