f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b

Discussion in 'Calculator Requests' started by math_celebrity, Jan 25, 2017.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b

    Set up both equations with values
    When x = 3, f(3) = 17, so we have a(b)^3 = 17
    When x = 7, f(7) = 3156, so we have a(b)^7 = 3156

    Isolate a in each equation
    a = 17/(b)^3
    a = 3156/(b)^7

    Now set them equal to each other
    17/(b)^3 = 3156/(b)^7

    Cross Multiply
    17b^7 = 3156b^3

    Divide each side by b^3
    17b^4 = 3156

    Divide each side by 17
    b^4 = 185.6471
    b = 3.6912
     

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