6.13 The logistic equation

The logistic equation can be used to model population growth, where $N(t)$ signifies the number of individuals in a population at time $t$. The idea is that for a small population ($N\ll K$) the growth rate is roughly proportional to $N$, but as $N$ increases then competition for resources slows the growth rate (or increases the death rate), i.e. as $N$ tends towards $K$ then the factor $1-N/K$ tends to zero, reducing the growth rate towards zero.