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Potens funktion med a og b – Bliv bedre og lær det på 3 min!

Vi har i denne artikel valgt, at fokusere på potensfunktion. Emnet potensfunktion er svært for mange studerende. Det skyldes at mange studerende har svært ved at skelne mellem en potensfunktion og en eksponentiel funktion. Vi giver dig svaret på hvad en potens funktion er her.

En potensfunktion har forskriften:

Potensfunktion 1

Potensfunktionens forskrift kan afbildes som en graf. Indtegnes potensfunktionen på dobbelt logaritmisk papir, så vil det blive til en ret linje. a (eksponenten) og b (konstantleddet) i en potensfunktion kan beregnes ud fra to punkter.

 

Det er vigtigt at kunne kende en potensfunktion. Lad os tage et eksempel, som er en tidligere eksamensopgave taget fra et matematik hf eksamenssæt niveau c.

 

Eksempel

Lydniveauet for et bestemt musikanlæg kan beskrives ved modellen

Potensfunktion 2

hvor v er volumen for musikanlægget, og dB er lydniveauet for musikanlægget (målt i decibel).

Grafen for potensfunktionen er vist her:

Potensfunktion 3

Måden hvorpå man kan kende en potensfunktion er ved at a, er det tal der bliver opløftet. I vores eksempel er eksponenten a = 1,5.

 

Træn flere opgaver i potens funktion med vores anerkendte matematik træner –  Træn rigtige eksamensopgaver og scor topkarakter i matematik!

Opret bruger nu

 

Beregning af eksponenten a i potensfunktionen ud fra to punkter (x1 , y1) og (x2 , y2)

Man kan beregne eksponenten a i en potensfunktion ved hjælp af to punkter. Hvis man ved punkterne (x1 , y1) og (x2 , y2) ligger på grafen for potensfunktionen kan a beregnes ved;

Potensfunktion 4

Hvis vi tager eksemplet ovenfor med musikanlægget, og vi ved at punkterne (1 , 0,5) og ( 4 , 4) ligger på grafen (se grafen for potensfunktionen), så beregnes eksponenten a som følger;

Potensfunktion 5

Som det kan ses har vi påvist at man ved hjælp af to punkter som ligger på grafen på potensfunktionen kan beregne eksponenten a (Det samme som vores model eksempel).

Når vi kender eksponenten a og et punkt på grafen kan man beregne b i potensfunktionen.

 

Lær fremgangsmåderne i eksamens opgaverne. Flere end 90% af vores brugere mener at kunne opnå en bedre karakter til matematik eksamen – hvorfor vente? Kom igang nu med vores anmelderroste matematik træner!

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Beregning af b (konstantleddet) i en potensfunktion

Hvis man kender et vilkårligt punkt på grafen (x1 , y1) og eksponenten a, så kan b (konstantleddet) ud fra følgende formel;

Potensfunktion 6

Hvis vi igen tager fat i vores eksempel med musikanlægget, så ved vi at de to punkter (1 , 0,5) og ( 4 , 4) ligger på grafen for potensfunktionen. Vi kender eksponenten a = 1,5 (den har vi lige beregnet). Vi anvender punktet (1 , 0,5) i vores beregning af b (konstantleddet). Vi indsætter i formlen for b her:

Potensfunktion 7

Hvis vi havde anvendt vores andet punkt som ligger på grafen for potensfunktionen (4 , 4), så vil vi nå frem til samme resultat. Det vises herunder;

Potensfunktion 8

Læs mere: Simpel gennemgang af lineær funktion – Lær det her på ingen tid!,  Nem gennemgang af renters rente (kapitalfremskrivning)Få gode råd til eksamen – Læs om guldkornene her!

Er det nemmere at forstå potens funktion nu?

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