Bob asked in Science & MathematicsMathematics · 2 months ago

Does anyone know how to solve this?

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  • Philip
    Lv 6
    2 months ago

    y = a(b^x).

    (0,-1)........on y ---> -1 = a(b^0) = a, ie., -1 = a(1) = a.  Then a = -1

    (2,-0.25)...on y ---> -0.25 = -(b^2). Then b^2 = (1/4) and b = (+/-) (1/2).

    Now (-2,-4) on the graph is shown to be on y. Therefore -4=-[(-1/2)^(-2)]...(1). or

    -4 = -[(1/2)^(-2)]...(2).

    For (1) holding, 4 = -(1/2)^(-2) = -[2^(-1)]^(-2)] = -2^[(-1)(-2)] = -2^(2) = -4 which is not

    true. Therefore b =/= -(1/2).

    For (2) holding, 4 = (1/2)^(-2) = [2^(-1)]^(-2) = 2^[(-1)(-2)] = 2^(2) = 4 which is true.

    Therefore b = (1/2).

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  • ?
    Lv 6
    2 months ago

    You have y = a*b^x and you also know that (0,-1) and (2,-.25) are also on the curve.

    Start with (0,-1)

    -1 = a*b^0

    -1 = a*1

    a = -1

    y = (-1)b^x, use (2,-.25) to find b:

    -.25 = (-1)*b^2

    b^2 = .25

    b = .5

    • Bob2 months agoReport

      Thank you very much

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