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Samenvatting Getal&Ruimte HavoA hoofdstuk 9
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Samenvatting van het boek Getal & Ruimte, HavoA deel 3, hoofdstuk 9
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Wiskunde Hoofdstuk 9Lineaire groei
- Hoeveelheid per tijdseenheid neemt met hetzelfde getal toe
- Formule N = at + b, waarin a toename per tijdseenheid is; b is
beginhoeveelheid
- Is in de grafiek een rechte lijn
Vraag:
De hoeveelheid N groeit lineair. Op t = 5 is N = 130 en op t = 8 is N = 190.
Stel de formule op van N.
Uitwerking:
N = at + b
ΔN 190−130
a= = = 20
Δt δ−5
N = 20t + b
130 = 20 x 5 + b
b = 30
N = 20t + b
Exponentiële groei
- De tijdseenheid wordt met een vast getal vermenigvuldigd
Groeifactor: Het getal waarmee steeds wordt vermenigvuldigd
- Hierbij hoort de formule N = b x g2
Voorbeeld:
In de formule N = 800 x 1,3t
Is 800 de beginhoeveelheid en 1,3 de groeifactor
Tabellen bij exponentiële groei
Jaar 1998 2002 2006 2010 2014
Aantal km 17 600 21 500 26 200 32 000 39 000
21500 26200
Exponentiële groei is 1,22 want, = 1,22 en = 1,22 en
17600 21500
32000 39000
= 1,22 en = 1,22
26200 32000
Formule is dus L = 17 600 x 1,22t
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