Right now this is all theoretical and assumes that every bacteria reproduces every generation.
From the start of this I am going to write my two function:
Model of the growth of a bacteria colony from another source, given that the source give 1000 bacterium.
C(t) = (1000)(2^t)
Derivative of that function:
C'(t) = (1000)(2t)^(t-1)
Model of growth of a bacteria colony starting from scratch (10 bacteria).
C(t) = (10)(2^t)
Derivative of that function:
C'(t) = (10)(2t)^(t-1)
It is a lot easier for new bateria to grow under this condtion C(t) = (1000)(2^t) than under this condition C(t) = (10)(2^t) when C (colony) is a function of t (time) and the base is assuming how many bacteria there are on the filter when t=0 aka when the tank is set up for the case of the second function and 1000 colonies in the first because the Bio-spira or other culture was added.
By looking at these functions, we can quickly see how fast a tank cycles when we seed it with bacteria. With these models, seeding a tank that requires 1 billion bacteria takes 3/4 of the time. If you want the math you just have to solve for t when C = 10^9.
Anyone else check this? What do you all think? Someone with a degree? I am only a senior in highschool!
From the start of this I am going to write my two function:
Model of the growth of a bacteria colony from another source, given that the source give 1000 bacterium.
C(t) = (1000)(2^t)
Derivative of that function:
C'(t) = (1000)(2t)^(t-1)
Model of growth of a bacteria colony starting from scratch (10 bacteria).
C(t) = (10)(2^t)
Derivative of that function:
C'(t) = (10)(2t)^(t-1)
It is a lot easier for new bateria to grow under this condtion C(t) = (1000)(2^t) than under this condition C(t) = (10)(2^t) when C (colony) is a function of t (time) and the base is assuming how many bacteria there are on the filter when t=0 aka when the tank is set up for the case of the second function and 1000 colonies in the first because the Bio-spira or other culture was added.
By looking at these functions, we can quickly see how fast a tank cycles when we seed it with bacteria. With these models, seeding a tank that requires 1 billion bacteria takes 3/4 of the time. If you want the math you just have to solve for t when C = 10^9.
Anyone else check this? What do you all think? Someone with a degree? I am only a senior in highschool!
