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    Rearranging an Algebraic Formula: Bass Curve

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    I have a formula, known as the Bass Curve Formula, that I would like rearranged. The formula generates an S curve that initially grows slowly, then accelerates before slowing down and plateauing. (See example)

    I would like the formula to be rearranged to find a variable (p).

    Please find the attached file for a detailed explanation.

    Re-arranging an Algebraic Formula

    BrainMass,

    I am a 30 year business manager and therefore my algebra is very rusty indeed.

    I have a formula, known as the Bass Curve, that I would like re-arranging. The formula generates an S curve that initially grows slowly, then accelerates before slowing down and plateau-ing. (See example)

    The standard Arrangement of the Formula is:

    Nt = Nt-1 + p.(m - Nt-1) + q. Nt-1.(m - Nt-1)/q

    Where:

    Nt = Current population no.

    Nt-1 is last year's population no.

    m is the maximum threshold

    And p and q are constants

    I would like to re-arrange the formula to find p.

    It should be a straightforward exercise for an experienced maths person but like I said my algebra is rusty.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:40 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/rearranging-algebraic-formula-bass-curve-variable-5072

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    Solution Preview

    We can rewrite this formula as follows.

    N_(t)-N_(t-1)=pm+(m-p)N_(t-1)-[N_(t-1)]^2
    =[p+N_(t-1)][m-N_(t-1)] ......(1)
    =-[N_(t-1)-(m-p)/2]^2+[(m+p)/2]^2. ...

    Solution Summary

    An algebraic formula is rearranged.

    $2.49

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