“Population Growth”的概念、定义、习题解题方法及翻译-数学辞典

单词

Population Growth

释义

Population Growth

The differential equation describing exponential growth is

(1)

This can be integrated directly

(2)

(3)

Exponentiating,

(4)

Defining

gives

in (4), so

(5)

The quantity

in this equation is sometimes known as the Malthusian Parameter.

Consider a more complicated growth law

(6)

where

is a constant. This can also be integrated directly

(7)

(8)

(9)

Note that this expression blows up at

. We are given the Initial Conditionthat

, so

(10)

The

in the Denominator of (10) greatly suppresses the growth in the long runcompared to the simple growth law.

The Logistic Growth Curve, defined by

(11)

is another growth law which frequently arises in biology. It has a rather complicated solution for

See also Gompertz Curve, Life Expectancy, Logistic Growth Curve, Lotka-Volterra Equations,Makeham Curve, Malthusian Parameter, Survivorship Curve

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