Hey to all, to start: thank you for taking your time to read this. Basically I am trying to include breeding in a model for a breeding farm. The only problem is it gets extremely complicated (with all pictures included in this post matching excel files will be provided at the end). I think the easiest way to explain this would be to dive straight into it. I want to create a mathematical model where you can change the time required to become fertile and the length in which each animal is fertile. I have already created a model in which ten percent of fertile animals breed after six months once but I am looking to adjust it so they can breed for two or more months once they are fertile. Below is a image (sorry if its not uploaded correctly) of the first 25 terms (each term is equivalent to one month and it takes exactly one month for them to breed). It is unfinished and shows just how long it would take to do by hand as it is a tedious process.

comp.jpg

To simplify the model for you guys (I am not interested in the final method, just the way to get their) I will use this model as a demo: y = 1000e-0.041x. As you can see when graphed it decays over time.

HeIZRLU.png

Basically, after six months a new function will be created with 10% of that population the month before and the y value (total weight, that is what the function is representing) and to calculate the y value to graph each one will be summed. An example of this can be seen in the picture below (the excel file is also attached).

HQeyFfR.png

(Ignore the fact that their are two functions, these are the ones I want to apply this to but they get a bit complicated :L. I am just wondering if anyone had any ideas to enable me to make it so I can adjust the time to become fertile after birth and how many times, once they are fertile they can breed.

I do really apologize if this is confusing but their is no easy and straight forward way to explain it, hopefully the attached excel file will explain to you what I am trying to accomplish more clearly than I am being right now.
demo.xlsx

Thank you again, hopefully someone will understand what I am trying to accomplish.