Population growth models - Revision history

Michael at 11:50, 8 June 2011

2011-06-08T11:50:00Z

← Older revision		Revision as of 11:50, 8 June 2011
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	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	var brd = JXG.JSXGraph.initBoard('box1', {~~originX~~: 10, ~~originY: 250~~, ~~unitX: 40~~, ~~unitY: 20~~, axis:true});		var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.25, 12.5, 14.75, -12.5], axis:true});
	var t = brd.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
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	===The JavaScript code===		===The JavaScript code===
	<source lang="~~xml">~~		<source lang="javascript">
	~~<jsxgraph height="500" width="600" board="board" box="box1~~">		var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.25, 12.5, 14.75, -12.5], axis:true});
	var brd = JXG.JSXGraph.initBoard('box1', {~~originX~~: 10, ~~originY: 250~~, ~~unitX: 40~~, ~~unitY: 20~~, axis:true});
	var t = brd.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
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	}		}
	}		}
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 20:44, 29 September 2010

2010-09-29T20:44:38Z

← Older revision		Revision as of 20:44, 29 September 2010
Line 16:		Line 16:

	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		var brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.~~createElement~~('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.~~createElement~~('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.~~createElement~~('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	var e = brd.~~createElement~~('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});		var e = brd.create('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();

	A = 5;		var A = 5;
	tau = 0.3;		var tau = 0.3;

	function clearturtle() {		function clearturtle() {
Line 58:		Line 58:
	<source lang="xml">		<source lang="xml">
	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		var brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.~~createElement~~('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.~~createElement~~('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.~~createElement~~('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	var e = brd.~~createElement~~('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});		var e = brd.create('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();

	A = 5;		var A = 5;
	tau = 0.3;		var tau = 0.3;

	function clearturtle() {		function clearturtle() {

A WASSERMANN at 14:51, 14 July 2010

2010-07-14T14:51:11Z

← Older revision		Revision as of 14:51, 14 July 2010
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	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Turtle Graphics]]		[[Category:Turtle Graphics]]
			[[Category:Calculus]]

A WASSERMANN at 07:50, 23 June 2009

2009-06-23T07:50:14Z

← Older revision		Revision as of 07:50, 23 June 2009
Line 60:		Line 60:
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);

	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
Line 66:		Line 65:

	t.hideTurtle();		t.hideTurtle();

			A = 5;
			tau = 0.3;

	function clearturtle() {		function clearturtle() {
Line 81:		Line 83:

	function loop() {		function loop() {
	var dy = alpha.Value()t.~~pos[1]~~dx; // Exponential growth		var dy = alpha.Value()t.Y()dx; // Exponential growth
	t.moveTo([dx+t.~~pos[0]~~,dy+t.~~pos[1]~~]);		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += dx;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);
	}		}

	}		}
	</jsxgraph>		</jsxgraph>

A WASSERMANN at 07:49, 23 June 2009

2009-06-23T07:49:43Z

← Older revision		Revision as of 07:49, 23 June 2009
Line 18:		Line 18:
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);

	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
Line 42:		Line 41:

	function loop() {		function loop() {
	var dy = alpha.Value()t.~~pos[1]~~dx; // Exponential growth		var dy = alpha.Value()t.Y()dx; // Exponential growth
	t.moveTo([dx+t.~~pos[0]~~,dy+t.~~pos[1]~~]);		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += dx;		x += dx;
	if (x<20.0) {		if (x<20.0) {

A WASSERMANN at 07:42, 23 June 2009

2009-06-23T07:42:53Z

← Older revision		Revision as of 07:42, 23 June 2009
Line 21:		Line 21:
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.Value()x);}],{strokeColor:'red'});		var e = brd.createElement('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();

A WASSERMANN at 07:42, 23 June 2009

2009-06-23T07:42:24Z

← Older revision		Revision as of 07:42, 23 June 2009
Line 42:		Line 42:

	function loop() {		function loop() {
	var dy = alpha.Value()t.pos[1]~~delta~~; // Exponential growth		var dy = alpha.Value()t.pos[1]dx; // Exponential growth
	t.moveTo([dx+t.pos[0],dy+t.pos[1]]);		t.moveTo([dx+t.pos[0],dy+t.pos[1]]);
	x += dx;		x += dx;

A WASSERMANN at 07:41, 23 June 2009

2009-06-23T07:41:39Z

← Older revision		Revision as of 07:41, 23 June 2009
Line 21:		Line 21:
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.X()x);}],{strokeColor:'red'});		var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();
Line 34:		Line 34:

	function run() {		function run() {
	t.setPos(0,s.X());		t.setPos(0,s.Value());
	t.setPenSize(4);		t.setPenSize(4);
	~~delta~~ = 0.1; // global		dx = 0.1; // global
	x = 0.0; // global		x = 0.0; // global
	loop();		loop();
Line 42:		Line 42:

	function loop() {		function loop() {
	var y = alpha.X()t.pos[1]delta; // Exponential growth		var dy = alpha.Value()t.pos[1]delta; // Exponential growth
	t.moveTo([~~delta~~+t.pos[0],y+t.pos[1]]);		t.moveTo([dx+t.pos[0],dy+t.pos[1]]);
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);
Line 64:		Line 64:
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.X()x);}],{strokeColor:'red'});		var e = brd.createElement('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();
Line 74:		Line 74:

	function run() {		function run() {
	t.setPos(0,s.X());		t.setPos(0,s.Value());
	t.setPenSize(4);		t.setPenSize(4);
	~~delta~~ = 0.1; // global		dx = 0.1; // global
	x = 0.0; // global		x = 0.0; // global
	loop();		loop();
Line 82:		Line 82:

	function loop() {		function loop() {
	var y = alpha.X()t.pos[1]~~delta~~; // Exponential growth		var dy = alpha.Value()t.pos[1]dx; // Exponential growth
	t.moveTo([~~delta~~+t.pos[0],y+t.pos[1]]);		t.moveTo([dx+t.pos[0],dy+t.pos[1]]);
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);

A WASSERMANN: /* Exponential population growth model */

2009-05-12T18:13:15Z

Exponential population growth model

← Older revision		Revision as of 18:13, 12 May 2009
Line 4:		Line 4:
	<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y </math>.		<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y </math>.

	With <math>\Delta \to 0</math> we get		With <math>\Delta t\to 0</math> we get
	<math> \frac{d y}{d t} = \alpha\cdot y </math>, i.e. <math> y' = \alpha\cdot y </math>.		<math> \frac{d y}{d t} = \alpha\cdot y </math>, i.e. <math> y' = \alpha\cdot y </math>.

A WASSERMANN: /* Exponential population growth model */

2009-05-12T18:12:05Z

Exponential population growth model

← Older revision		Revision as of 18:12, 12 May 2009
Line 1:		Line 1:
	===Exponential population growth model===		===Exponential population growth model===
	In time <math> \Delta t</math> the population grows by <math>\alpha\cdot y </math> elements:		In time <math> \Delta t</math> the population consisting of <math>y</math> elements grows by <math>\alpha\cdot y </math> elements:
	<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>.