Population growth models: Difference between revisions
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===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>, that is | |||
<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 16:06, 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 $\Delta \to 0$ we get:
- [math]\displaystyle{ \frac{d y}{d t} = \alpha\cdot y }[/math]
i.e.
- [math]\displaystyle{ y' = \alpha\cdot y }[/math]
The initial population is $y(0)= s$.
