Difference between revisions of "Population growth models"

From JSXGraph Wiki
Jump to navigationJump to search
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:
+
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>
+
<math> \Delta y = \alpha\cdot y\cdot \Delta t </math>, that is
It follows:
+
<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:
 
With $\Delta \to 0$ we get:
 
:<math> \frac{d y}{d t} = \alpha\cdot y </math>
 
:<math> \frac{d y}{d t} = \alpha\cdot y </math>
 
i.e.
 
i.e.
 
:<math> y' = \alpha\cdot y </math>
 
:<math> y' = \alpha\cdot y </math>
 +
The initial population is $y(0)= s$.
 
<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 17:06, 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 $\Delta \to 0$ we get:

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

i.e.

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

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