# Population growth models

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### 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 $y(0)= s$.