Calculator Example 1

A discrete dynamical system is given by:

u(n) = 0.7u(n-1) + 3
u(0) = 1

  1. Make a table with values for the function u when n = 0, 5, 10, 15, etc.
  2. Calculate u(30) and u(50).
TI-83/TI-84 Instructions:
  • Press MODE
  • Select Seq instead of Func on the 4th line
  • Press Y=
  • Enter
    • nMin = 0
    • u(n) = 0.7u(n-1) + 3 (To enter u, press 2nd-7. To enter n, press the button labeled X,T,theta,n.)
    • u(nMin) = {1}
  • Press WINDOW
  • Enter
    • nMin = 0
  • Press 2nd - TBLSET
  • Enter
    • TblStart = 0
    • Δ Tbl = 5
    • Indpnt: Auto
    • Depend: Auto
  • Press 2nd - TABLE
  • You should find that u(30) ≅ 9.999797146 and u(50) ≅ 9.999999838. You will need to use the arrows to scroll down to u(50) and you will need to move the cursor over the function value if you want more decimals than the rounded off value shown.
TI-89 Instructions:
  • Press MODE
  • Under Graph, select Sequence instead of Function
  • Select Y=
  • Enter
    • u1 = 0.7u1(n-1) + 3
    • ui1 = 1
  • Press WINDOW
  • Enter
    • nmin = 0
  • Select TBLSET
  • Enter
    • tblStart.....0
    • Δ tbl....5
    • Graph <-> Table: OFF
    • Independent....Auto
  • Select TABLE
  • You should find that u(30) ≅ 9.9997971459374 and u(50) ≅ 9.9999998381382. You will need to use the arrows to scroll down to u(50) and you will need to move the cursor over the function value if you want more decimals than the rounded off value shown.