Population growth models: Difference between revisions

Revision as of 16:05, 22 April 2009

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]

@@ Line 1: / Line 1: @@
 ===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>
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