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# 什麼是logistic growth equation

什麼是logistic growth equation？其中各元素的意義是？麻煩各位大大

### 1 Answer

- kinsdaLv 71 decade agoFavorite Answer
Logistic Growth (equation 5) dN/dt = N [(b0 - kbN) - (d0 + kdN)]We need to modify the basic equation 1 so that birth and death rates are no longer constant through time, but decrease and increase respectively as population size increases: where kb and kd are the density-dependent birth and death rate constants respectively. This equation predicts that a population will stop growing (zero population growth) when birth rate equals death rate, or: (equation 6) b0 - kbN = d0 + kdN This can be converted into an equation showing the size at which the population reaches a steady state: (equation 7) N = (b0 - d0) / (kb + kd) The value of N when the population is at steady state is the carrying capacity of the environment, or K. This can be simplified: (equation 8) K = r / (kb + kd) since b0 - d0 = r. If we combine this new form of the carrying capacity equation with equation 5 we get the familiar form of the logistic growth equation: (equation 9) dN/dt = rN [(K - N) / K]