# penality function: The growth of a population highly depends on its starting size

#### needsmathhelpnow

##### New member
I have a real world problem where i select populations based on growth. The growth of a population highly depends on its starting size, e.g. small populations grow faster than already large populations. Now i want do not only want small populations in my selection but also large ones because growth in those populations is harder to archive.

Is there any mathematical functions that has a parameter that i can tune?

#### needsmathhelpnow

##### New member
Maybe i need to elaborate here.
Given is the following data:
 population growth last month 200 500% 150 45% 2500 28% 7000 15%
My current logic is just select everything that grew more than 30% last month. But what i actually want is a function that selects based on population grow, in other words the bigger the population is the smaller the growth has to be to be selected.

I think that is a common problem, i just cant wrap my head around it.

#### stapel

##### Super Moderator
Staff member
I have a real world problem where i select populations based on growth. The growth of a population highly depends on its starting size, e.g. small populations grow faster than already large populations. Now i want do not only want small populations in my selection but also large ones because growth in those populations is harder to archive.

Is there any mathematical functions that has a parameter that i can tune?
Maybe i need to elaborate here.
Given is the following data:
 population growth last month 200 500% 150 45% 2500 28% 7000 15%
My current logic is just select everything that grew more than 30% last month. But what i actually want is a function that selects based on population grow, in other words the bigger the population is the smaller the growth has to be to be selected.

I think that is a common problem, i just cant wrap my head around it.
"Populations" of what? "Select" how? If you are selecting "based on growth", can't you find the growth and then do the selecting?

In what manner do the smaller populations grow faster than the larger populations? If you are selecting based on high growth, how is that supposed to fit into selecting slow-growth populations?

It would probably help if you provided us the all the information upon which you're trying to develop a model. When you reply, please include a clear listing of your thoughts and efforts so far, as well as your current level of mathematical study.

Thank you!

Eliz.

#### Steven G

##### Elite Member
Maybe i need to elaborate here.
Given is the following data:
 population growth last month 200 500% 150 45% 2500 28% 7000 15%
My current logic is just select everything that grew more than 30% last month. But what i actually want is a function that selects based on population grow, in other words the bigger the population is the smaller the growth has to be to be selected.

I think that is a common problem, i just cant wrap my head around it.
This table is contradicting what you said. Clearly a population of 150 is smaller than a population of 200, but according to what you said, the smaller population should grow more quickly. Your table shows the opposite. What do you have to say about that?

#### needsmathhelpnow

##### New member
This is just an example. Lets say i have thousands of populations ranging from 2k to 600k. It is easier for a small population, to double in size, than for a already large population.

I am selecting the 10 populations that grew the most every week.
Right now i have a rigid rule: return me the 10 populations that grew the most. (as a recommendation)

The problem is that it almost always returns me 10 small populations, but i would like to select larger populations that still had good growth (e.g. 20%) as well.

Intuitively i would like to penalize the growth of small populations or boost the growth of larger populations without using rigid brackets.

EDIT:
I think one way to achieve this would be to use a weighted growth metric. Maybe i could multiply the growth by the logarithm of the population size.

Last edited:

#### stapel

##### Super Moderator
Staff member
This is just an example. Lets say i have thousands of populations ranging from 2k to 600k....
Please realize that this sounds as though you are seeking the services of a data-mining or -modelling company, rather than for hints and helps on math homework...?

Eliz.

#### blamocur

##### Senior Member
I think one way to achieve this would be to use a weighted growth metric. Maybe i could multiply the growth by the logarithm of the population size.
This sounds like one way to get closer to your goals.
But there are infinite number of functions (of the population size and its growth) which would satisfy your criterion. If I had a practical problem like this I'd come up with at least several such functions and see which ones produce results I like the most.