• % • • • • & $ (# % "

!# "

$$

' # "

!# "

) $$ !# * + , -

* # * % # ( # (# " *

!# *

! " .

% %

-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 +