[size=150]Die Exponentialfunktion f mit der Gleichung [math]y=0,1\cdot2^x[/math] beschreibt die Entwicklung der Faltung, wobei nach x Faltungen die Dicke y mm beträgt. ([math]x\in\mathbb{R}^+_0,y\in\mathbb{R}^{+}[/math])[/size][br][br][b]Aufgabe 1:[/b][br]Erstelle mithilfe des GGB-Grafikrechners ([url=https://www.geogebra.org/graphing]Link[/url]) eine Wertetabelle für die ersten fünf Faltungen, d. h. [math]0\le x\le5;\, \Delta x=1[/math].
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[/img]
[size=150] [br] [br] [br]Wir betrachten nun die Exponentialfunktion f: y = 0,1·2[sup]x[/sup] [u]nicht mehr im Sachzusammenhang der Faltung[/u].[br]D. h. für die nachfolgenden Aufgaben gilt: [math]x,y\in\mathbb{R}[/math][br][/size][br][b]Aufgabe 2:[/b][br]a) Stelle die Exponentialfunktion f grafisch dar. Verwende den GGB-Grafikrechner.[br][br]b) Lass dir zusätzlich die Graphen zu folgenden Funktionen anzeigen:[br][list][*]Quadratische Funktion p mit y = 0,1x² [/*][*]Lineare Funktion g mit y = 0,1x[/*][/list]Betrachte die Unterschiede der Graphen.
[size=150] [br] [br]Gegeben sind Exponentialfunktionen mit Gleichungen der Form y = [color=#0000ff]k[/color]·[color=#ff00ff]a[/color][sup]x[/sup] [/size]mit [math]x,y\in\mathbb{R};k\in\mathbb{R}\backslash[/math]{0};[math]a\in\mathbb{R}^+\backslash[/math]{1}.[br][br][b]Aufgabe 3:[/b][br]Untersuche die Bedeutung der Parameter [b][color=#0000ff]k[/color][/b] und [b][color=#ff00ff]a[/color][/b].[br]Stelle die beiden Schieberegler so ein, dass der [color=#ff0000][b]Graph der Exponentialfunktion[/b][/color] genau durch die angegebenen [b][color=#00ff00]Punkte der Faltung[/color][/b] verläuft.[br]
[b]Aufgabe 4:[/b][br][br]a) Für [b]a > 1[/b] ...
[size=85]Zur Erinnerung: "[i]der Graph steigt[/i]" heißt: "[i]Ich laufe auf dem Graph von links nach rechts und es geht nach oben.[/i]"[/size]
b) Für[b] 0 < a < 1[/b] ...
c) Der [b]Parameter k[/b] gibt an, ...