User:Miguelsxvi/sandbox

Stable population
A stable population is one whose growth rate and age structure stays constant in time. Therefore, the share of the total population that falls in a certain age group does not change.

In discrete time, having a constant growth rate $$\frac{P^{t+1}-P^t}{P^t} = c$$ results in an exponential growth of the population $$P^{t+n} = (1+c)^nP^{t}$$, increasing or decreasing. Furthermore, in a closed population (no migration), the crude mortality rate and the crude birth rate change by the same amount every year

$$c=\frac{P^{t+1}-P^t}{P^t} = \frac{B^{t}-D^t}{P^t} = \text{CBR}^t-\text{CMR}^t$$

The same is true in continuous time, where the growth rate would be expressed like $$\frac{d}{dt}P(t)= c P(t)$$ leading to $$P(t) = P(0)e^{ct}$$.

Stationary population
A population is considered stationary if its growth rate is zero and the age structure is constant. It is particular case of a stable population.