Texas Instruments PLUS TI-89 - Manual (Page 157)

140 Chapter 9: Sequence Graphing
09SEQUEN.DOC TI-89/TI-92 Plus: Sequence Graphing (English) Susan Gullord Revised: 02/23/01 10:59 AM Printed: 02/23/01 2:14 PM Page 140 of 14
Steps
³
TI-89
Keystrokes
›
TI-92 Plus
Keystrokes Display
1. Display the MODE dialog box.
For Graph mode, select
SEQUENCE .
3
B 4
¸ 3
B 4
¸
2. Display and clear the Y= Editor.
Then define the sequence as
u1(n) = iPart(.8 ù u1(n ì 1)+1000) .
Use iPart to take the integer part of
the result. No fractional trees are
harvested.
To access iPart( , you can use
2 I , simply type it, or select it
from the CATALOG .
¥ #
ƒ 8 ¸
¸
2 I 1 4
. 8 j U 1 c
j N | 1 d «
1 0 0 0 d ¸ ¥ #
ƒ 8 ¸
¸
2 I 1 4
. 8 U 1 c
N | 1 d «
1 0 0 0 d ¸
3. Define ui1 as the initial value
that will be used as the first
term.
¸
4 0 0 0 ¸ ¸
4 0 0 0 ¸
4. Display the Window Editor. Set
the n and plot Window variables.
nmin=0 and nmax=50 evaluate the
size of the forest over 50 years.
¥ $
0 D 5 0 D
1 D 1 D ¥ $
0 D 5 0 D
1 D 1 D
5. Set the x and y Window variables
to appropriate values for this
example.
0 D 5 0 D
1 0 D 0 D
6 0 0 0 D
1 0 0 0 0 D 5 0 D
1 0 D 0 D
6 0 0 0 D
1 0 0 0
6. Display the Graph screen. ¥ % ¥ %
7. Select Trace . Move the cursor to
trace year by year. How many
years (
nc ) does it take the
number of trees ( yc ) to stabilize?
Trace begins at nc=0.
nc is the number of years.
xc = nc since n is plotted on the x
axis.
yc = u1(n), the number of trees at
year n.
…
B
and A
as necessary
…
B
and A
as necessary
Preview of Sequence Graphing
A small forest contains 4000 trees. Each year, 20% of the trees will be harvested (with 80%
remaining) and 1000 new trees will be planted. Using a sequence, calculate the number of
trees in the forest at the end of each year. Does it stabilize at a certain number?
Initially After 1 Year After 2 Years After 3 Years . . .
4000 .8 x 4000
+ 1000
.8 x (.8 x 4000 + 1000)
+ 1000
.8 x (.8 x (.8 x 4000 + 1000) + 1000)
+ 1000
. . .
By default, sequences use
the Square display style.