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Composition of functions

  1. Sep 7, 2008 #1
    1. The problem statement, all variables and given/known data
    If you invest x dollars at 4% interest compounded annually, then the amount A(x) = 1.04x. Find A o A, A o A o A, and A o A o A o A. What do these compositions represent? Find a formula for the composition of n copies of A.


    2. Relevant equations
    f o g = f(g(x))


    3. The attempt at a solution
    Okay, well, I'm trying to work this out and I get really stuck.
    If I do A(A(x)), that's A(A(x)) = 1.04(1.04x) correct? I'm not sure at all "what these compositions are supposed to represent. Please help!
     
  2. jcsd
  3. Sep 7, 2008 #2

    nicksauce

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    Correct for A(A(x)).

    Hint: If I have x dollars to start with, how many do I have after year 1? After year 2 and 3?
     
  4. Sep 7, 2008 #3
    OH okay. I think I get it. So when they ask to find each composition, I just put A(A(x)), then A(A(A(x))) and so on?

    I get that each composition represents the TOTAL amount that is invested up to year 2, 3, 4 and so on, but how do I find the formula for n copies of A?
     
  5. Sep 7, 2008 #4

    HallsofIvy

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    Just as you say, A o A= (1.04)(1.04x)= (1.04)2x. So A o A o A= (1.04)(1.04)2x= (1.04)3x. A o A o A o A= (1.04)(1.04)3x= (1.04)4x. Now, suppose you had A o A o A o A o A o A o A o A, with eight A's. What would that be?
     
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