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Math Help - finding values from power functions

  1. #1
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    finding values from power functions

    I need help on this math problem. I keep getting the wrong answers for the values for n and a.

    Given a power function of the form f(x)=axn , with f(3)=18 and f(6)=72, find n and a .
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    Quote Originally Posted by jojoferni244 View Post
    I need help on this math problem. I keep getting the wrong answers for the values for n and a.

    Given a power function of the form f(x)=axn , with f(3)=18 and f(6)=72, find n and a .
    From 18=a\cdot 3^n you get 3^n=\dfrac{18}{a}

    Re-write

    72 = a\cdot 6^n~\implies~72=a\cdot 2^n \cdot 3^n

    Now substitute the term of 3^n in the 2nd equation:

    72=a\cdot 2^n \cdot \dfrac{18}{a}~\implies~2^n=4~\implies~n=2

    Plug in this value into one of the given equations and solve for a. You'll get a = 2

    A shortcut:

    72 = a\cdot 6^n
    18=a\cdot 3^n

    Divide both equations columnwise:

    \dfrac{72}{18}=\dfrac{6^n}{3^n} = 2^n~\implies~ n=2
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