Fish, Cycling, and a whole lotta MATH!

[CHOMPERS]

Radley, Highschool huh? I am totally impressed. I am rusty on the population modeling but the equation looks right (less a proportionality constant for death rate/birth rate). I sold my precalculus book (dumb thing to do). It had good info that I often needed to refer back to. My calculus book has some on population modeling but I can not find it in the index. I'll look more later and post what I find. I did some modeling in differential equations but I am not sure if that will help. It is 2:30am and I am over due for an appointment with my pillow.

 

[RadleyMiller]

firstly,kudo's for getting a grip on calculus.

But to me there are to many variables to work it out accurately...

How old are you? should you be surfing the net for porn, instead of posting calculus on a fish forum

thanks,

hahaha, I will do that later

Radley, Highschool huh? I am totally impressed. I am rusty on the population modeling but the equation looks right (less a proportionality constant for death rate/birth rate). I sold my precalculus book (dumb thing to do). It had good info that I often needed to refer back to. My calculus book has some on population modeling but I can not find it in the index. I'll look more later and post what I find. I did some modeling in differential equations but I am not sure if that will help. It is 2:30am and I am over due for an appointment with my pillow.

Thanks CHOMPERS, I am trying to get this somewhat right so we have something to refer to when we talk to new people about cycling and why and how it works. Please get some sleep. We can work on all of this later.

BTW, my calc book is sitting next to me, but I have no plan whatsoever on opening it.

 

[CHOMPERS]

Radley,
The differential equation that models the growth of a population is dp/dt=kp where dp/dt is the differential of the population in respect of time, k is the proportionality constant for the growth rate, and p is the population at a given time.

This assumes that the birth rate and death rate changes directly as the population changes (i.e. one bacteria will always divide into two bacteria, and for every 100 bacteria that divide Y bacteria will die). In other words, letting k1 be the birth rate and k2 be the death rate, the population grows by k1 - k2 = k bacteria.

Differential equations may be solved to initial conditions such as p(0)=Po, meaning the function p of t (at time zero) is equal to p-naught (the initial population). If a mass bacteria kill occurs, the time can be set to zero with the initial population being the remaining bacteria.

The differential equation dp/dt=kp is a first order equation and solves like a derivative/anti-derivative. Taking the definite integral of both sides with respect to time gives the function
p(t)=Po*e^(kt).
Where Po is the initial population, and e is the logarithmic function e. Ya gotta think back a year or two. The value of e is something like 2.73 but I am guessing. I know it is 2.something. That is what scientific calculators are for.

At this point, the equation is useless because we do not have a constant for k. Two conditions are needed to solve the equation for k, the initial population and the population at time t. Solving for k,
k={ln(P)-ln(Po)}/t
where t is the time measured from the initial population to the measured growth.

Now who wants to count bacteria.

 

[RadleyMiller]

Radley,
The differential equation that models the growth of a population is dp/dt=kp where dp/dt is the differential of the population in respect of time, k is the proportionality constant for the growth rate, and p is the population at a given time.

This assumes that the birth rate and death rate changes directly as the population changes (i.e. one bacteria will always divide into two bacteria, and for every 100 bacteria that divide Y bacteria will die). In other words, letting k1 be the birth rate and k2 be the death rate, the population grows by k1 - k2 = k bacteria.

Differential equations may be solved to initial conditions such as p(0)=Po, meaning the function p of t (at time zero) is equal to p-naught (the initial population). If a mass bacteria kill occurs, the time can be set to zero with the initial population being the remaining bacteria.

The differential equation dp/dt=kp is a first order equation and solves like a derivative/anti-derivative. Taking the definite integral of both sides with respect to time gives the function
p(t)=Po*e^(kt).
Where Po is the initial population, and e is the logarithmic function e. Ya gotta think back a year or two. The value of e is something like 2.73 but I am guessing. I know it is 2.something. That is what scientific calculators are for.

At this point, the equation is useless because we do not have a constant for k. Two conditions are needed to solve the equation for k, the initial population and the population at time t. Solving for k,
k={ln(P)-ln(Po)}/t
where t is the time measured from the initial population to the measured growth.

Now who wants to count bacteria.

WTF? Haha, now I am confused. I need to finish high school before I get to that stuff. Some of this stuff makes sense but the differential equations through me through a loop as I am sure it did to everyone else. I tried to make this a pretty simple exponential growth function and you turned this into some pretty complicated stuff.

Have we accomplished anything more than proving it takes a tank to cycling faster with old media and that a lot of MFKers do not like math? I think that is all we have done, and we have done a great job.


It seems like we may be able to close this with a little bit of Latin:

quod erat demonstrandum

Unless anyone else has anything to add, I think we have been able to accomplish this goal. Now I have to go model the spread of the H5N1 virus across the world, see you all later.

for all of you that do not know, H5N1 is bird flu!