Growth Procedures
There are different ways to describe growth procedures.
- Linear growth
- Exponential growth
- Logical table growth (a mixture from exponential and limited growth)
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 |
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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 |
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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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