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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.

##### Solution Summary

An algebraic formula is rearranged.

##### 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. ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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