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-82 Instructions:
  • Press MODE
  • Select Seq instead of Func on the 4th line
  • Press Y=
  • Enter
    • Un = 0.4Un-1 + 0.6Vn-1 + 6 (Your calculator uses Un-1 instead of u(n-1) and Vn-1 instead of v(n-1). To enter this press 2nd-7 and 2nd -8.)
  • Press WINDOW
  • Enter
    • UnStart = 10
    • VnStart = 20
    • nStart = 0
  • Press 2nd - TBLSET
  • Enter
    • TblMin = 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.