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Growth Procedures

There are different ways to describe growth procedures.

  1. Linear growth
  2. Exponential growth
  3. Logical table growth (a mixture from exponential and limited growth)
  4. In nature, there mostly are logical growth procedures.

    kind of growth function equations (explicit) model of growth procedures
    Linear growth f(x) = dx + f(0) Znew = Zold + c
    Exponential growth f(x) = f(0) * qx Znew = Zold * c
    Logical table growth / Znew = Zold * c * (K - Zalt)

    Terms
    function equations model of growth procedures
    d = growth rate c = constant
    q = growth factor K = maximum (saturation deficiency)
    f(0) = Initial value Z = variable of state
    f(x) = condition for value x
    x = time
     

    Linear growth

    An oil tank contains 800 l oil. Per minute, 200l of oil are pumped into the tank.


    d = 200
    f(0) = 800
    x = time in minute

    f(x) = 200x + 800

    Exponential growth

    A yeast culture with 5g yeast trebles once per hour its mass.


    q = 3
    f(0) = 5
    x = time in hours

    f(x) = 5 * 3x

    Logical table growth:

    A population of frogs grows logistically. 1 is the maximum population (100%) and 0 stands for no frogs (0%). Logically the population grows slowly if there are many frogs. In the middle it reaches his highest growth point. To the end the frogs increase more slowly. (less food).

    Zneu = Zalt * c * (K - Zalt)

    K = 1

    Initial value = 0,1 (10%)

    c = between 1 and 3 (=2)

    c = between 3 and 3,57 (3,4)

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