Renter - page 11
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It's quiet, or I don't have time for it :)
I've added the conditions of the problem there.
Let's solve it from here.
That's right. Next...
Or is the relationship negative ? - Increasing withdrawals into the pocket - automatically decreases the growth of the deposit.
in the given conditions -- exactly positive !
You're confusing yourself... As long as we do the analysis without pocketing -- i.e. what constitutes such a system !
And about exponential growth, I assumed you set that condition a priori.
Well, whatever. Let it be negative and severe - not the point.
What's new in your statement? We have:
Substitute qa for k and we arrive at the same equations I have:
With the same problems.
.
In our particular case G(s)=0
and the equations are simplified by
Now, applying the inverse Laplace transform, we get the result:
.
here we have the exponent as a result, not as a destination.
.
That's it - it's clear how the system behaves.
Now we can go on to consider the second part of the problem -- turning on the valve and separating the flow.
.
zy.
I'll get to that today, but a little later...
P.S.In case anyone is interested, here is the global census data from Goskomstat for the entire history of mankind:
Year million people.
I had to logarithm twice to get this graph, but even then the growth is faster than a straight line. This means that the relationship is even faster than exp(exp(t))
I had to logarithm twice to get this graph, but even then the growth is faster than in a straight line. This means that the dependence is even faster than exp(exp(t))
Yes, the correlation is interesting.
In the 90's S.P. Kapitsa (the one who hosts the show "Obvious incredible") came to us with a report on the population of the earth. It is interesting that according to his model, which at that time fit the historical data well, dN/dt=N^2 and predicted an explosive growth of the population in 2025 (the so-called Malthusian catastrophe if I am not mistaken). In general, to fulfill the condition of the above difurcation, it is necessary that every woman of reproductive age gives birth to a child from every man :-) It is under these conditions that the equality of the growth rate to the square of the total population would be fulfilled. Which seems insane. Then I realised it was a consequence of fitting the model to the available data. And if you don't take the data before 1945. And if you don't take data before 1945 (where you can see a birth rate spike), but work on a more or less calm period from 1945 to now, then there is no catastrophe:
Moreover, it can be seen that the global population is asymptotically tending towards an equilibrium level of 11 billion and will reach that level in about 100 years.
It has to be equated to zero and solved with respect to k.