Share
Explore BrainMass

Rearranging an Algebraic Formula: Bass Curve

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.

Attachments

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.

$2.19