# Difference between revisions of "Population growth models"

### Exponential population growth model

In time $\Delta y$ the population grows by $\alpha\cdot y$ elements: $\Delta y = \alpha\cdot y\cdot \Delta t$, that is $\frac{\Delta y}{\Delta t} = \alpha\cdot y$. With $\Delta \to 0$ we get:

$\frac{d y}{d t} = \alpha\cdot y$

i.e.

$y' = \alpha\cdot y$

The initial population is $y(0)= s$.