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Math Help - affine difference/solution equations

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    Question affine difference/solution equations

    Hey! I am having a problem in my math class understanding affine/difference equations...I can give you an example right out of my text book of one of the problems I'm struggling with:

    For each affine difference equation and initial condition, find the solution equation.
    a) p(n) = 2.5p(n-1)+900; p(0)= 400 - p(0) is the initial condition
    b) p(n) = 0.75p(n-1) - 45; p(0) = 510
    c) p(n) = 1.03p(n-1) - 75; p(0) = 75

    Maybe it's just me, but i have no idea where to start. I have looked at examples in the first few pages of the chapter, only to be led to the wrong answer! Can anyone help??
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    Quote Originally Posted by emilyerin88 View Post
    Hey! I am having a problem in my math class understanding affine/difference equations...I can give you an example right out of my text book of one of the problems I'm struggling with:

    For each affine difference equation and initial condition, find the solution equation.
    a) p(n) = 2.5p(n-1)+900; p(0)= 400 - p(0) is the initial condition
    b) p(n) = 0.75p(n-1) - 45; p(0) = 510
    c) p(n) = 1.03p(n-1) - 75; p(0) = 75

    Maybe it's just me, but i have no idea where to start. I have looked at examples in the first few pages of the chapter, only to be led to the wrong answer! Can anyone help??
    For difference equations of the form

    p_n = k \,p_{n-1}

    one typically tries a solution of the form p_n = c \,\rho^n and find the \rho that works. For equations of the form

    p_n = k \,p_{n-1} + A

    where A is a constant, first try p_q = q_n + \alpha and try and find \alpha such that the new equation becomes q_n = k q_{n-1}.

    Try that and see how you make out.
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