1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook