Difference between revisions of "Population growth models"
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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: | |
| − | :<math> \Delta | + | :<math> \Delta y = \alpha\cdot y\cdot \Delta t </math> |
| − | :<math> \frac{ | + | 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> | ||
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Revision as of 17:05, 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]
