Preview Of Sequence Graphing - Texas Instruments TI-89 Manual Book

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
4000 .8 x 4000
+ 1000
Steps
1. Display the
MODE
For mode, select
Graph
SEQUENCE .
2. Display and clear the Y= Editor.
Then define the sequence as
u1(n) = iPart(.8ù u1(nì 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 .
3. Define ui1 as the initial value
that will be used as the first
term.
4. Display the Window Editor. Set
the and Window variables.
n plot
nmin=0 and nmax=50 evaluate the
size of the forest over 50 years.
5. Set the x and y Window variables
to appropriate values for this
example.
6. Display the Graph screen.
7. Select Trace . Move the cursor to
trace year by year. How many
years ( ) does it take the
nc
number of trees (
yc
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.
140 Chapter 9: Sequence Graphing
After 2 Years
.8 x (.8 x 4000 + 1000)
+ 1000
TI-89
Keystrokes
3
dialog box.
B 4
¸
¥ #
ƒ 8 ¸
¸
.
2 I 1 4
. 8 j U 1 c
j N | 1 d «
1 0 0 0 d ¸
¸
4 0 0 0 ¸
¥ $
0 D 5 0 D
1 D 1 D
0 D 5 0 D
1 0 D 0 D
6 0 0 0 D
1 0 0 0
¥ %
...
B and
as necessary
) to stabilize?
After 3 Years
.8 x (.8 x (.8 x 4000 + 1000) + 1000)
³ ›
TI-92 Plus
Keystrokes
3
B 4
¸
¥ #
ƒ 8 ¸
¸
2 I 1 4
. 8 U 1 c
N | 1 d «
1 0 0 0 d ¸
¸
4 0 0 0 ¸
¥ $
0 D 5 0 D
1 D 1 D
0 D 5 0 D
1 0 D 0 D
6 0 0 0 D
1 0 0 0
¥ %
...
A B and A
as necessary
+ 1000
Display
By default, sequences use
the Square display style.
. . .
. . .