Summary
Zusammenfassung exponentieller Wachstum
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ExponenziellerWachstum-> exponenzialfunktion
-> H VOR 0 1 =
Übungsaufgaben:
-> h von
1 = 2 S. 87,10 S. 87, 11 S. 87,13
-> 7 VOR 24 Wachstum a) a) No 5.1,1 a)
243b=
i
=
= .
.
it..........
-> 7 von 3 8 =
f(x) 5.1/X
=
b)0,0016 b4
=
1
-... 0.2 D
=
b) f(30) 5.1./30
=
4 -
f(30) 87,24cm
2- er Potenzer 2004 =b"
=
-> i
-
f(31) 5.1,131
-> N(x) bx
=
=
f(31) 9 5,97cm
H(x) Anzal
=
=
derZeit b) f(x) 10.bx =
b:Um wie viel es wird
mehr =Bei 5
0,5
10.b2
=
b2
=
. 1, 0,7 b
=
=
* y 7
->
b< 1 exponenziellerZerfall
=
= f(x) 10.0,77 =
->
allgemeint f(x) bx
=
C3 y
10.0,720
=
y 0,00797 mg
=
· ah
Beispiel:
No 2.500.000.000
=
Bettenspicaie
N1 2.500.000.000. = 1,050
N() =
2.500.000.000. 1,0161
Addition Multiplikation
N(x) n.bY =
Addition
Addition
SEE ALGEN
Sco) Aco) 3m2
ots
= =
+10% pro tag
( E) 3. Migt
S(t) --.7 A =
=
800
+
Linear:gleicherBetrag
Quadratisch: von der Zeit
abhängig
Exponenziell:immer mitdem selben Faktor, hängtvon der Zeit,explosionsartig"
Eine Funktion mitderVorschriftf(x):a.b*m i ta e , a 0, b>0 und
=
bel heit
Exponentialfunktion zurBasis b.
Wachstumsprozesse, die man mithilfe von Exponential funktionen beschreiben
kann, bezeichnetm a n als exponentielles Wachstum mitdem
Anfangswert a und dem Wachstumsfaktorb mitbo.
Im Falle von b sprichtm a n von expentioneller zunahme.
S. 45,5
a) Anfangswert =
4 b) Anfangswert:25
Wachstumsfaktor: Wachstumsrate:
R.: f(t) 4.bt
=
R.: f(t) 25.bt
=
10 4.651 4
=
12,5 25.b =
- 0
1 25
(=) 2,5 65 =
l ==> 0,5=b *
E) 1,2 b=
E) 1,07 b=
Wachstumsfaktor:1 12
1,07
Wachstumsfaktor =
: :
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