Please help me work out how many cats I'll end up with in a set period.?

[labrat0088]

I'm trying to make a flier to educate our community (which is over run with feral cats) on the benefits of sterilization. I have adopted 7 cats and can't take on anymore. There are 100's more out there roaming around our town.I contacted an animal shelter that gives numbers of how cat populations get out of control to use their figures, but am not allowed. I must source it myself, but can't find the info.So, my question is: If I start with 1 male and 1 female cat, they have 3 litters in a year, and produce their 1st litter at 6 month s of age, having approx 5 kittens per litter, how many will I end up with in say, 5 years if all of their offspring and so on down the line reproduce at this rate? Bear in mind that approx 1/2 will be female.I'm an animal technician, so I'm seeing this as a community service. I hope some maths minded people out there can see it as a puzzle to work out. Thanks in advance.

[MathManTG]

This problem was solved in slightly different form back in 1202 by Leonardo Fibonacci, giving rise to the Fibonacci numbers, one of the most wonderful things in all of mathematics.It's fairly complicated to work out exact numbers, but what it comes down to is exponential growth.The numbers you give are explosive, so the percentage increase is huge.Each pair produces 15 kittens per year, 7.5 times as many as you start with, or 750 %.Let's say they wait a full year instead of 6 months to start.At the end of year 2, they have added 15.At the end of year 3, they have added another 15,and the first 15 have added 112.5 (never mind what .5 cats means or the fact that it is an odd number).At the end of year 4, another 15, another 112.5, and 843.75 on top of that.At the end of year 5, ANOTHER 15, 112.5, 843.75 + 6328.125.You can see where this is headed.These numbers are not exact, because they do everything year by year rather than every 4 or 6 months,but it gives an idea of how fast exponential growth is.They also don't take into account that eventually the cats stop reproducing. As long as births exceed deaths, the numbers keep going up.The human population is increasing by "just" 3% per year, nowhere near 750%, and you can see how many of us there are.For perhaps a more realistic set of numbers, instead of increasing by 7.5 times, use "only" 3 or 4.If each pair produces 6 kittens instead of 15,2, 2+6, 2+6+24, 2+6+24+96, 2+6+24+96+384 = (2, 8, 32, 128, 512)With 8 kittens instead of 15,2, 2+8, 2+8+40, 2+8+40+200, 2+8+40+200+1000 = (2, 10, 50, 250, 1250...)

[K-Dub0252]

Things don't exactly line up right, so let me make a few modifications on the cautious side.First, I will refer to the kittys as male/female (breeding) pairs. Since 5 per litter is odd, I will change each litter to 2 pair of kittens (4 total).Also, I will change the maturation period to 8 months, that is, a pair of cats' first offspring will be born eight months after their birth.The breakdown is done in four-month periods, and is composed of three numbers: # of newborn pairs, # of 4-month pairs, # of adult pairs.Now# of newborn pairs → # of 4-month pairs the next period# of 4-month pairs + # of adult pairs → # of adult pairs the next period.2 * (# of 4-month pairs + # of adult pairs) → # of newborn pairs the next period.We start with one pair of 4-month kittens.0, 1, 0 (← year 0)2, 0, 12, 2, 16, 2, 3 (← year 1)10, 6, 522, 10, 1142, 22, 21 (← year 2)86, 42, 43170, 86, 85342, 170, 171 (← year 3)682, 342, 3411366, 682, 6832730, 1366, 1365 (← year 4)That's 5461 pair of cats (10922 total), after 4 years, i.e. population explosion.For the adult pairs, # of adults in nth generation= # of adults in (n-1)th generation + 2*(# of adults in (n-2)th generation)(e.g. 85 = 43 + 2*21)The newborn pairs is twice the adult pairs, and the four-month pairs are the newborns from 4 months prior.I guess someone should check my work lolThis is just a model. There are many factors not included here, in particular mortality/infertility rates.Hope this helps.♣ ♣