Could someone please help me with this math problem?

The question gives me this hill function: y= Ax^n/(k^n+x^n)

The question is as so: For what positive value(s) of x does y achieve half its value at the horizontal asymptote?

1 Answer

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  • Anonymous
    1 month ago
    Favorite Answer

    I'll assume n>1.

    For large values of x, k^n becomes negligible compared to x^n and we get:

    y = Ax^n/x^n = A

    So y=A is the horizontal asymptote.

    When y = A/2:

    A/2= Ax^n/(k^n+x^n)

    k^n+x^n = 2x^n

    k^n = x^n

    x = k

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