Population growth models: Difference between revisions

From JSXGraph Wiki
No edit summary
No edit summary
Line 1: Line 1:
===Exponential population growth model===
===Exponential population growth model===
 
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 16:05, 22 April 2009

Exponential population growth model

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

[math]\displaystyle{ \Delta y = \alpha\cdot y\cdot \Delta t }[/math]

It follows:

[math]\displaystyle{ \frac{\Delta y}{\Delta t} = \alpha\cdot y }[/math]

With $\Delta \to 0$ we get:

[math]\displaystyle{ \frac{d y}{d t} = \alpha\cdot y }[/math]

i.e.

[math]\displaystyle{ y' = \alpha\cdot y }[/math]