Mer geogebra: Skillnad mellan sidversioner
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Versionen från 7 maj 2013 kl. 07.20
Exponentialfunktioner
Jämför
Jämför med den allmänna formen för andragradsfunktionen:
- [math]\displaystyle{ y = ax^2 + bx + c }[/math] (bortse från de sista termerna)
- [math]\displaystyle{ y = ax^2 }[/math] (a är en konstant, vi kan lika gärna skriva c)
- [math]\displaystyle{ y = C \cdot x^2 }[/math] (tänk nu att vi kastar om x och 2, C är en konstant )
- [math]\displaystyle{ y = C \cdot 2^x }[/math] (här har vi ett exempel på en exponentialfunktion)
- [math]\displaystyle{ y = C\cdot 1.5^x = C \cdot (\frac{3}{2})^x }[/math] (Vi kan ha olika tal som höjs upp i x)
- [math]\displaystyle{ y = C \cdot 0.5^x = C \cdot (\frac{1}{2})^x = C \cdot (2^{-1})^{x}= C \cdot 2^{-x} }[/math]
på generell form:
- [math]\displaystyle{ y = C \cdot a^x }[/math]
- talet a kallas basen. x är exponenten
Växande
Tänk på pengar på banken med ränta varje år. Pengarna växer med ränta på ränta. 15 % innebär en tillväxtfaktor om 1.15 (förändringsfaktorn). Antag att man har 2000 kr från början. Tillväxten blir då exponentiell. Det tar bara fem år till en fördubbling.
Filen ligger på HD.