Curves {logistic curve} can model growth with growth factors and limiting resources. Growth can depend on growth factors, which can have weights. Limiting resources {bottleneck, growth} can slow growth.
Amount or percentage P at time t is P(t) = A * (1 + m * e^(-t/T)) / (1 + n * e^(-t/T)), where A = constant growth-factor weight, m = original growth-factor amount, n = original limiting-resource amount, and T = time period or inverse growth rate.
Growth is percentage of factor to resource. Denominator and numerator decrease at same rate.
beginning
Original amount depends on relative m and n amounts and on weight A: P(0) = A * (1 + m) / (1 + n). If n is much greater than m and A, denominator is large, and P is zero.
process
At first, growth is exponential with time. Then growth passes through time when growth has constant rate and is linear. Then growth slows exponentially to zero. Amount is then maximum or 100 percent at maturity.
shape
Logistic curve has sigmoid shape.
comparison
Logistic function inverts natural logit function.
Mathematical Sciences>Geometry>Plane>Curve>Kinds>Logistic
3-Geometry-Plane-Curve-Kinds-Logistic
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Date Modified: 2022.0224