# Need a Second Function to Limit the Growth of an Exponential Function

#### greenapplestoo

##### New member
I am writing a computer program, a population simulator, where I start with a population of about 30 people, then let them pair off and have children. After watching a few generations, its clear they reproduce at an exponential rate. I haven't computed tan approximate function which describes this growth, but I suspect it can be described as an N^X function.

My problem is my population grows without limit. In real life, there are other factors which keep a population from growing forever: limited resources, wars, social mechanisms, etc. I to build that into my program somehow.

Let's say my unlimited exponential growth is described by some function f(x):

Code:
f(x) = N^x

What I'd like is some secondary function, g(x), which I can multiply (or add or whatever) against f(x) that allows for initial exponential growth, but eventually introduces an upper bound which the combined function cannot overcome. Put graphically:

I didn't think this would be a hard problem, but when I cast about and to come up with my own g(x), the second function either does not really limit population growth, or it flattens it completely. Any suggestions for a g(x) which might accomplish what I seek?

Many thanks

#### Dr.Peterson

##### Elite Member
I am writing a computer program, a population simulator, where I start with a population of about 30 people, then let them pair off and have children. After watching a few generations, its clear they reproduce at an exponential rate. I haven't computed tan approximate function which describes this growth, but I suspect it can be described as an N^X function.

My problem is my population grows without limit. In real life, there are other factors which keep a population from growing forever: limited resources, wars, social mechanisms, etc. I to build that into my program somehow.

Let's say my unlimited exponential growth is described by some function f(x):

Code:
f(x) = N^x

What I'd like is some secondary function, g(x), which I can multiply (or add or whatever) against f(x) that allows for initial exponential growth, but eventually introduces an upper bound which the combined function cannot overcome. Put graphically:

View attachment 9417
I didn't think this would be a hard problem, but when I cast about and to come up with my own g(x), the second function either does not really limit population growth, or it flattens it completely. Any suggestions for a g(x) which might accomplish what I seek?

Many thanks
Do a search for "logistic growth". I think that's exactly what you want; it is not a simple combination of exponential and something else, but a distinct function that combines the features you want.

#### greenapplestoo

##### New member
Do a search for "logistic growth". I think that's exactly what you want; it is not a simple combination of exponential and something else, but a distinct function that combines the features you want.
Ahhh... yes, this looks perfect, thank you professor. It will be tricky to translate this into my program, but no-where near as challenging as devising the curve itself. You've done me a huge favor, thank you.