Difference between revisions of "Population growth models"

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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 $y(0)= s$.
 
<html>
 
<html>

Revision as of 17:07, 22 April 2009

Exponential population growth model

In time [math] \Delta y[/math] the population grows by [math]\alpha\cdot y [/math] elements: [math] \Delta y = \alpha\cdot y\cdot \Delta t [/math], that is [math] \frac{\Delta y}{\Delta t} = \alpha\cdot y [/math].

With [math]\Delta \to 0[/math] we get: [math] \frac{d y}{d t} = \alpha\cdot y [/math], i.e. [math] y' = \alpha\cdot y [/math].

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