Nombre max d'années

Valeur initiale

taux d'évolution

Valeur initiale

variation absolue

vinter

Agrandir(-Nbans/10,  -n*(1+taux/100)^Nbans/5, Nbans,n*(1+taux/100)^Nbans)

tickLabels = Sequence[Text[k+ “T_2”, (0,-0.5) + (k Tdoublement, -0.1)], k, 2, Nbans/Tdoublement]

T_2

Temps de doublement

Nombre de doublements

Comparaison avec une croissance arithmétique

Voir intersection

Vue initiale

voirinter = false
Nbans = 61 (slider from 2 to 100, step 1)
n = 10 (slider from 1 to 20, step 1)
taux = 4.5 (slider from 0 to 10, step 0.1)
b = 15 (slider from 0 to 20, step 1)
r = 3.51 (slider from 0.01 to 20, step 0.01)
l7 = Solve((n * (1 + taux / 100)^(x)) = b + (r * x))
sol2 = Element(l7, 2)
Sol2 = Intersect(sol2, y = 0)
Maxans = If(Defined[Sol2], Max[Nbans, x(Sol2)] + 2, Nbans)
g(x) = (n * (1 + taux / 100)^(x))
f(x) = b + (r * x)
F = Intersect(f, g, (Nbans, f(Nbans)))
E = Intersect(f, g, (-1.6206591745367096, 9.311486297376149))
tpsdep: floor(Max[x(E), x(F)]) + 3
e = false
A: (0, n)
texte2: "+" + (LaTeX[taux]) + " \, %"
Tdoublement: log(2) / log(1 + taux / 100)
C: (Tdoublement, 0)
l1 = Sequence(((k * Tdoublement), 0), k, 1, Nbans / Tdoublement)
a = false
texte4: "
T_2\approx" + (LaTeX[Tdoublement]) + "\ \text{ans}"
i = 1 (slider from 1 to If[e, floor(Maxans / Tdoublement) + 1, floor(Nbans / Tdoublement) + 1], step 1)
l4 = Sequence(Segment[((t * Tdoublement), 0), ((t * Tdoublement), (2^(t) * n))], t, 1, i)
l2 = Sequence(Sequence[((t * Tdoublement), (k * n)), k, 1, 2^(t)], t, 1, i)
l3 = Sequence(Segment[((t * Tdoublement), (n * 2^(t))), (((t + 1) * Tdoublement), (n * 2^(t)))], t, 0, i - 1)
l5 = Sequence(Segment[((t * Tdoublement), (n * 2^(t - 1))), (((t + 1) * Tdoublement), (n * 2^(t - 1)))], t, 1, i - 1)
c = Defined(E)
d = false
l6 = Sequence((k, (r * k) + b), k, 0, Maxans)
VMaxans = If(voirinter, Nbans, Maxans)
h = Max(l7)
sol1 = Element(l7, 1)
Lpts = Sequence((k, (n * (1 + taux / 100)^(k))), k, 0, If[Defined[Sol2], Maxans, Nbans])
voirboutonvue = false
D = If(¬voirinter, (Maxans / 3, ((0.7 * n) * (1 + taux / 100)^(Maxans))), (Nbans / 3, ((0.7 * n) * (1 + taux / 100)^(Nbans))))
D2 = If(voirinter, (Nbans / 4, ((0.7 * n) * (1 + taux / 100)^(Nbans))), (Maxans / 4, ((0.7 * n) * (1 + taux / 100)^(Maxans))))
B = If(voirinter, (Nbans / 3, ((-n) * (1 + taux / 100)^(Nbans) / 8)), (Maxans / 3, ((-n) * (1 + taux / 100)^(Maxans) / 8)))
C_1 = Corner(1, 1)
C_2 = Corner(1, 2)
C_3 = Corner(1, 3)
C_4 = Corner(1, 4)
XMIN: x(C_1)
YMIN: y(C_1)
XMAX: x(C_3)
YMAX: y(C_3)
G: ((2 * C_1) + (0 * C_2) + (3 * C_3) + (3 * C_4)) / 8
H: ((15 * C_1) + (6 * C_2) + C_3 + C_4) / 16
tickLabels = Sequence(Text[k + "T_2", (0, ((-n) * (1 + taux / 100)^(Nbans) / 20)) + ((k * Tdoublement) - Nbans / 80, -0.1)], k, 2, Nbans / Tdoublement)