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 | + | |
| − | + | 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>. |
| − | + | ||
The initial population is $y(0)= s$. | The initial population is $y(0)= s$. | ||
<html> | <html> | ||
Revision as of 18:07, 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 $y(0)= s$.
