### Calculator Example 2

A discrete dynamical system is given by:

u(n) = 0.4u(n-1) + 0.6v(n-1) + 6
v(n) = 0.5u(n-1) + 0.2v(n-1) + 4
u(0) = 10
v(0) = 20

1. Make a table with values for the functions u and v when n = 0, 1, 2, 3, 4, etc.
2. Make a table with values for the functions u and v when n = 0, 5, 10, 15, 20, etc.
3. Calculate u(50) and v(50).
4. Calculate u(53) and v(53).

TI-83/TI-84 Instructions:
• Press MODE
• Select Seq instead of Func on the 4th line
• Press Y=
• Enter
• nMin = 0
• u(n) = 0.4u(n-1) + 0.6v(n-1) + 6 (To enter u and v, press 2nd-7 and 2nd-8 respectively. To enter n, press the button labeled X,T,theta,n)
• u(nMin) = {10}
• v(n) = 0.5u(n-1) + 0.2v(n-1) + 4
• v(nMin) = {20}
• Press WINDOW
• Enter
• nMin = 0
• Press 2nd - TBLSET
• Enter
• TblStart = 0
• Δ Tbl = 1 (for question #2, replace "1" with "5")
• Indpnt: Auto (for question #4, replace "Auto" with "Ask")
• Depend: Auto
• Press 2nd - TABLE
• You should find that u(50) ≅ 39.99 and v(50) ≅ 29.992. You will need to use the arrows to move the cursor over the function values if you want more decimals than the rounded off values shown.

TI-89 Instructions:
• Press MODE
• Under Graph, select Sequence instead of Function
• Select Y=
• Enter
• u1 = 0.4u1(n-1) + 0.6u2(n-1) + 6
• ui1 = 10
• u2 = 0.5u1(n-1) + 0.2u2(n-1) + 4
• ui2 = 20
• Press WINDOW
• Enter
• nmin = 0
• Select TBLSET
• Enter
• tblStart.....0
• Δ tbl....1 (for question #2, replace "1" with "5")
• Graph <-> Table: OFF
• Independent....Auto (for question #4, replace "Auto" with "Ask")
• Select TABLE
• You should find that u(50) ≅ 39.99 and v(50) ≅ 29.992. You will need to use the arrows to move the cursor over the function values if you want more decimals than the rounded off values shown.