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 $\Delta \to 0$ we get:
 
:<math> \frac{d y}{d t} = \alpha\cdot y </math>
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>.
:<math> y' = \alpha\cdot y </math>
 
The initial population is $y(0)= s$.
The initial population is $y(0)= s$.
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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 $y(0)= s$.