polynomial growth trends

[andyfw]

Does anyone know how to project polynomial growth trends in excel - ie a
growth rate that initially accelerates and then tapers off after a period -
to trend towards an absolute population size (no further growth) after a
further period.

 

[Jerry W. Lewis]

It is rarely accurate to extrapolate beyond the data, unless you know the
correct form of the equation. Your verbal description does not sound like a
polynomial, which necessarily goes to +/- infinity as the independent
variable goes to +/- infinity.

Jerry

 

[Gary''s Student]

Consider using something like:

y = a * exp( b * (1-1/x)) rather than a polynomial. This has only two
parameters and has the desired limited growth characteristic.

 

[Herbert Seidenberg]

Since you say that the curve initially accelerates,
I visualize the curve as an "S" curve.
Maybe like this:
http://en.wikipedia.org/wiki/Generalised_logistic_curve
Here is the formula in Excel:
y=k_a+k_c/((1+k_t*EXP(-k_b*(x-2*k_m)))^(1/k_t))
where
y= population
x= time
k_a lower asymptote
k_c upper asymptote minus k_a
k_m time of maximum growth
k_b growth rate
k_t asymmetry of max growth time

A simplified formula might look like this:
y=a/(b+EXP(-c*x))