Population Growth

Consider a population $P(t)$ of individuals — human, insect, or bacterial — at time $t$, with a constant birth rate and a constant death rate. The rate at which the population changes is simply the difference between how fast individuals are being added (births) and how fast they are being removed (deaths), giving the differential equation

where $k$ is the net rate constant (birth rate minus death rate), taken as constant over the period being modeled. This is exactly the growth-and-decay equation from the previous section, so it solves the same way: $P(t) = P_0 e^{kt}$, where $P_0$ is the population at $t = 0$. …