Difference between revisions of "Population growth models"

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===Exponential population growth model===
 
===Exponential population growth model===
 
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In time <math> \Delta y</math the population grows by <math>\alpha\cdot y </math> elements:
:<math> \Delta{f} = \alpha\cdot \Delta t </math>
+
:<math> \Delta y = \alpha\cdot y\cdot \Delta t </math>
:<math> \frac{df}{dt} = \beta I S </math>
+
It follows:
 +
:<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>
 +
i.e.
 +
:<math> y' = \alpha\cdot y </math>
 
<html>
 
<html>
 
<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>
 
<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>

Revision as of 18:05, 22 April 2009

Exponential population growth model

In time [math] \Delta y\lt/math the population grows by \ltmath\gt\alpha\cdot y [/math] elements:

[math] \Delta y = \alpha\cdot y\cdot \Delta t [/math]

It follows:

[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]

i.e.

[math] y' = \alpha\cdot y [/math]