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) 
Z_{new }= Z_{old }+ c 
Exponential growth 
f(x) = f(0) * q^{x} 
Z_{new }= Z_{old }* c 
Logical table growth 
/ 
Z_{new }= Z_{old }* c * (K  Z_{alt}) 
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).
Z_{neu }= Z_{alt }* c * (K  Z_{alt})
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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