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Affine Recurrence Plotter

  • Affine Recurrence Plotter

    Grade: 6th to 8th, High School

    This tool can be used to graphically investigate the effects of parameters a, b, and c in the following affine recurrence relation:

    A(n) = b × A(n - 1) + c,   A(0) = a

    One possible use of this tool is to investigate the balance in a savings account that earns simple interest. If the account begins with $1000, earns 6% interest annually, and $50 is deposited each month, set a = 1000, b = 1.06, and c = 50. The graph will show the balance after n years.

    The affine recurrence plotter can also be used to investigate the population of a stocked trout pond, as described in the Trout Pond unit.

    Activity

    Instructions

    • When first opened, the tool appears in Graph view and shows the graph of:
    A(n) = b × A(n - 1) + c
    • You can change the values of a, b, and c by dragging the sliders. Alternatively, you can type in values for a, b, and c directly. (Note that you can enter values outside the range of the sliders. For instance, the slider for b goes from -2 to 2, yet you can type -13, 3, or 1000 into the box directly.)
    • In Window view, you can change the range of x- and y-values that are displayed in Graph view.
    • In Y= or Plots view, you can enter up to five standard equations and up to two recursive equations. (When first opened, the recursive equation A(n) = b × A(n - 1) + c is already entered into one of the recursive boxes.)

    Objectives and Standards

    NCTM Standards and Expectations
    • Algebra
    • 6-8
    • High School (9-12)
    • Algebra