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No, I don't understand what you have in mind yet. Tell me.
What kind of hard evidence is that?! It's obvious:
I'll make a detailed description so that the thought process is clear.
Oh! [Laughs]
Oh!
But first I have a question:
is there a clear understanding of where I got the idea that in this problem (with one capacity) we have an exponential growth in balance?
Incidentally, bankers and sociologists would be closer to this formulation of the problem:
The population of a country is increasing at a rate proportional to the number of people at a given time. Determine the number of population as a function of time.
.
All these problems -- about filling a deposit, a vessel, a country -- are equivalent, they differ only in linguistics ;)
But first I have to ask a question:
is there a clear understanding of where I got the idea that in this problem(with one capacitance) we have an exponential growth in balance?
You, if I'm not mistaken, had TWO capacities from the start:
And about exponential growth, I assumed you set that condition a priori.
Incidentally, bankers and sociologists would be closer to this formulation of the problem:
The population of a country grows at a rate proportional to the number of people at a given time. Determine the number of population as a function of time.
.
All these problems -- about filling a deposit, a vessel, a country -- are equivalent, they differ only in linguistics ;)
Indeed, the problems are similar. But what is different is the solution being sought. In the case of population, population size as a function of time. Diffur that describes this process: dN/dt=k*N, where k is a constant, N is the population. And the solution is the same as the one we obtained above for the volume of deposit f. There are no problems. They begin when we try to find an optimum of this function by an internal parameter, and here the analogy with population will not help us because it does not contain this parameter. If we introduce it artificially, we will face the same problem as in our original problem.
P.S. If anyone is interested, here is the data of census of the population of the world according to goskomstat for the whole history of mankind:
Year million people.
-35000 3
-15000 6
-7000 12
-2000 47
0 165
1000 310
1500 490
1650 608
1750 770
1800 871
1850 1130
1900 1659
1920 1811
1930 2020
1940 2295
1950 2466
1955 2752
1960 3019
1965 3336
1970 3698
1975 4080
1980 4450
1985 4854
1990 5292
1995 5765
1997 5900
2000 6130
2001 6207
2
:-)
Hello all!
I have been allowed to use a deposit of X0 rubles for t months. Every month a fixed percentage q of the current value of the deposit X is deposited. I'm allowed to withdraw a percentage k from the account every month, but it doesn't exceed the value of q.
So the task is to maximize the amount of money withdrawn over a period of t months. It seems obvious that withdrawing the whole accrued interest q every month is not the best option, because in this case the deposit does not grow and with less load on the account, the eventually withdrawn amount may be larger... On the other hand, the value of k should not go to zero, because in this case the amount withdrawn would also go to zero. Apparently, the truth is somewhere in the middle. But where exactly?
Help me solve this problem analytically in general terms.
P.S. I haven't posted in a branch of problems not related to trade, because the proposed topic is related to the latter.
First of all, let us carefully analyse the problem - what is set? What do we have? What do we determine?
That's right. Now...
Or is there a negative correlation? - Increase the inflow into your pocket - automatically decreases the growth of your deposit.
Maybe dig into 1s, maybe there is a solution to your problem?
Although I do not understand why you are solving it all day long, it means you suck at higher mathematics better go to the math forum, there are many wunderkinds sitting there, maybe they can help...