Business Essay

713 words - 3 pages

6.
6. Funktioner
Gør rede for eksponentialfunktionen, herunder grafen for funktionen og hvordan konstanterne i forskriften bestemmes. Du skal også komme ind på fordoblings- og halveringskonstanten.
A: Forklar kort hvad man forstår med eksponentialfunktionen fx=bax og giv et eksempel, f.eks. en konkret eksponentiel sammenhæng (henfald af radioaktivt stof, renteformlen, bakterievækst osv.).
B: Forklar hvilken betydning a og b har, og hvordan de grafisk ses i et koordinatsystem (b er skæringen/ startbetingelsen, a er fremskrivningsfaktoren og afgør, om der er tale om fald eller stigning). Forklar hvad halverings- og fordoblingskonstanten betyder, og opskriv formlerne til at finde dem.
...view middle of the document...

Så er der også fordoblings - og halveringstid.
Fordoblingstiden er den tidsmængde det tager for y at fordoble sig. t2 = log⁡(2)log⁡(a) Dette kan kun bruges på ting med en stigende værdi. Som for eksempel bakterie-mængder eller renteformlen. (altså en a-værdi over 1).
Og tilsvarende er halveringstiden det præcis omvendte, dette kan kun bruges på ting der har en a-værdi mellem 0 og 1 (a falder i dette tilfælde) som for eksempel henfald af radioaktivt stof og lignende.
t12= log⁡(12)log⁡(a)
Et eksempel områder kunne være vores forsøg med bakterier på en pølse;
Formlen hed her; y = 2,23 * 2,35x (tallene er i millioner).

Dette vil altså sige; at startværdien (b) er lig med 2,23 millioner.
Fremskrivningsfaktoren er her lig med 2,35 hvilket vil sige at bakteriemængden vokser med (2,35 -1) * 100 % om dagen. Dette er 135 %
Fordoblingstiden er lig med; log⁡(2)log⁡(2,35)= 0,81 dag
C; For at finde a og b bruger man de to ligninger der hedder:
b=y1a1x
A = x2-x1y2y1
Hvis man overfører dette til et konkret eksempel;
Om en eksponentiel funktion oplyses at;
p(1,5) og...

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