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Growth Curves
"Herbert Seidenberg" wrote: The s curve is modeled on the formula: =k_a+k_c/((1+k_t*EXP(-k_b*(x-k_m)))^(1/k_t)) where x =month k_a 0 lower asymptote (zero subscribers) k_b 0.5 growth rate k_c 560 upper asymptote minus k_a ( max subscribers) k_m 5 time of maximum growth (month # 5) k_t 0.2 asymmetry of max growth time Enter your numbers for k_a, k_c and k_m 0, 560 and 5 Enter guesses into k_b and k_t. Give the numbers defined names, using Insert Name Define or Create .... Create a sequence of numbers, the months, and name it xs: {0;1;2;3;4;5;6;7;8;9;10;11;12;13;14} Create a cell named MaxGrowth with this array formula: (enter it with CTRL+SHIFT+ENTER) =MAX(k_c*k_b*EXP(-k_b*(xs-k_m))/(1+EXP(-k_b*(xs-k_m)))^2) Tools Goal Seek Set Cell: MaxGrowth To Value: 70 By Changing Cell: k_b Create a cell named Start with this formulas: =k_a+k_c/((1+k_t*EXP(-k_b*(0-k_m)))^(1/k_t)) Tools Goal Seek Set Cell: Start To Value: 1 By Changing Cell: k_t Now all your coefficients are defined correctly and you can interpolate the number of subscribers at any time using the formula at the first line. Plotting this curve will help a lot. |
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