Taux d'évolution
707 mots
3 pages
• % • • • • & $ (# % "!# "
$$
' # "
!# "
) $$ !# * + , -
* # * % # ( # (# " *
!# *
! " .
% %
-1D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
# / *" ("
t 100
(# "
20 = 1040 5200 × 100
0 1 25 1 = = 0.25 2 25% = 100 4
3 2 4
-
y1
y2 5
y1 → y2 6
0
!
y1
y2
t=
y2 − y1 y1
/
1 2P − P P 100 t= = =1= = 100% P P 100 t < 0 ou y2 < y1 t > 0 ou y2 > y1
!" "#
7
" !# " -
# 1
8
• • •
0 0 0 #
1 9 %
!# " 1
$
: - 5 y1 y2 = (1 + t ) y1
6
!"
# $ $
% % (
&' %
y1 à y2
t=
/ 1 ' , ' " (&
y2 − y1 y1
y2 − y1 = t × y1 ⇔ y2 = ty1 + y1 ⇔ y2 = (1 + t ) y1
!# " * ' +
1−
10 = 0.9 100
&
'
)
! < ; # ), ' " (& ),
1−
19.6 = 1.196 100
&
-2D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
8
y1 y2 y1
&' ) ( 5
y2
-6
×c
y1 =! >
y2
0
y1
÷c
y2
0 "
.'
/
%
&" "
"
'
Rappels de Première : Applications
( * % !# " $$
Pi
• •
?! # " = !> = !? "!= ";
×0.9
= $"!
0
Pi
÷0.9
Pf
Pi =
1 Pf ≈ 1.11Pf 0.9 t ' = c '− 1 ≈ 0.11 = 11%
" ' 2 "
Pf
1 & " ' +
Pi 0
c ' ≈ 1.11
& '
y1 à y2
* , ! &
t c'= & &
y2 y2 à y1
y1
1 c 1 1+ t ' = 1+ t
( +
, , %
!# "
(# "
Pi
• c2 = 1 − 20% = 0.8
×0.9 ×0.8
c1 = 1 − 10% = 0.9
•
•
1 & "
0 A = !>
Pi → P2 → Pf
"@ ( = ? != "@ ? != $"( ( B 3 # " %
Pf = 0.9 × 0.8Pi = 0.72 Pi
% "
2 (&
(
% 4
%
-3D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
"
+
y1 à y2
* , 0 5 6
t1
y2 y1
y3 y3
t2 c = c1 × c2
×(1+ t2 )
y1 à y3
1 + t = (1 + t1 )(1 + t2 )
×(1+ t1 )
Pi → P2 → Pf
×(1+ t )
( + C
- , %
×(1+ 2% )
5
6
( #
! "
×(1+ 2% )
×(1+ 2% )
Pi → P2 ... → ... → P 10
×(1+ t )
0
1 + t = (1 + 2% ) = 1.02 ≈ 1.22
10 10
t ≈ 1.22 − 1 = 0.22
-
(# ( $
•
-
(1 +