# Population growth models

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:
$\frac{d y}{d t} = \alpha\cdot y$
$y' = \alpha\cdot y$
The initial population is $y(0)= s$.