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#1
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polynomial growth trends
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. |
#2
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polynomial growth trends
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 "andyfw" wrote: 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. |
#3
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polynomial growth trends
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. -- Gary''s Student - gsnu200762 "andyfw" wrote: 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. |
#4
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polynomial growth trends
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)) |
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