Population growth models: Difference between revisions
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<math> \Delta y = \alpha\cdot y\cdot \Delta t </math>, that is | <math> \Delta y = \alpha\cdot y\cdot \Delta t </math>, that is | ||
<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y </math>. | <math> \frac{\Delta y}{\Delta t} = \alpha\cdot y </math>. | ||
With | |||
With <math>\Delta \to 0</math> we get: | |||
i.e. | <math> \frac{d y}{d t} = \alpha\cdot y </math>, i.e. <math> y' = \alpha\cdot y </math>. | ||
The initial population is $y(0)= s$. | The initial population is $y(0)= s$. | ||
<html> | <html> | ||
Revision as of 16:07, 22 April 2009
Exponential population growth model
In time [math]\displaystyle{ \Delta y }[/math] the population grows by [math]\displaystyle{ \alpha\cdot y }[/math] elements: [math]\displaystyle{ \Delta y = \alpha\cdot y\cdot \Delta t }[/math], that is [math]\displaystyle{ \frac{\Delta y}{\Delta t} = \alpha\cdot y }[/math].
With [math]\displaystyle{ \Delta \to 0 }[/math] we get: [math]\displaystyle{ \frac{d y}{d t} = \alpha\cdot y }[/math], i.e. [math]\displaystyle{ y' = \alpha\cdot y }[/math].
The initial population is $y(0)= s$.
