If a population starts with 150 people, assuming all 150 can mate up until 75 years of age at their death, that makes 75 couples that can have 1 child per year. Say after 13 years a child can begin to mate. So after the first 13 years, 75 more people will be mating, about 37 more couples. What will the population be after 150 years? People die, but mate up to 75 years old. Every couple has 1 child per year. Mating begins at 13 years old.
Population growth: What will population be after 150 years?
- Thread starter pranzo
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People die when? No predators or disease? They all make it to 75?
How's the birth balance? 50M/50F? If you're having 75 kids the first year, there goes the 50% theory!
How about fecundity? Can EVERY new member of the society actually reproduce? Nothing ever goes wrong?
OK. This brings us to my real question. Why? Do you have a project? Are you trying to populate a remote space outpost?
It does seem like an interesting project for a simulation, but you will need way more assumptions.
How's the birth balance? 50M/50F? If you're having 75 kids the first year, there goes the 50% theory!
How about fecundity? Can EVERY new member of the society actually reproduce? Nothing ever goes wrong?
OK. This brings us to my real question. Why? Do you have a project? Are you trying to populate a remote space outpost?
It does seem like an interesting project for a simulation, but you will need way more assumptions.
Specifics
Ok, we are assuming that everyone lives to 75 and mates up until then. Nothing causes death besides this old age. There is an even split between male and female. So in the first year, if there are 75 children, then assume there are 37 new couples after 13 years that can now mate. Once there is a new odd number of offspring, then of course this is factored in with the extra one from the last batch. We can even safely assume that the extra one does not mate. So just take an even number of people to make the new couples each time.
Since nothing ever goes wrong as you say, everyone can mate. This is a problem of probability. What numbers could the population reach after 150 years given this formula?
I originally became interested in this problem after reading a random short story online, involving a race that went from 150 people to 190,000 in 150 years. I want to see if this is possible.
Ok, we are assuming that everyone lives to 75 and mates up until then. Nothing causes death besides this old age. There is an even split between male and female. So in the first year, if there are 75 children, then assume there are 37 new couples after 13 years that can now mate. Once there is a new odd number of offspring, then of course this is factored in with the extra one from the last batch. We can even safely assume that the extra one does not mate. So just take an even number of people to make the new couples each time.
Since nothing ever goes wrong as you say, everyone can mate. This is a problem of probability. What numbers could the population reach after 150 years given this formula?
I originally became interested in this problem after reading a random short story online, involving a race that went from 150 people to 190,000 in 150 years. I want to see if this is possible.
pka
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This is part of such a well known set of problems is recursive function.
But, who ever wrote this one didn’t do a very good job.
There are still a great many problems with you second post.
Look at the solution to the following:
http://www.freemathhelp.com/forum/viewtopic.php?t=7310&highlight=rats
The solution to your type of problem will be something like it.
But, who ever wrote this one didn’t do a very good job.
There are still a great many problems with you second post.
Look at the solution to the following:
http://www.freemathhelp.com/forum/viewtopic.php?t=7310&highlight=rats
The solution to your type of problem will be something like it.
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Well, if you just need a theoretical point of view, 190,000 is a piece of cake, even with death and disease. I took a very quick look at the first four generations and managed values in the neighborhood of 1,200,000. I lost track of what I was doing, so that may be couples, not individuals. I think 190,000 is nowhere near fantastic.
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Re: Formula
Please provide specifics. Thank you.
Eliz.
How far have you gotten on this? Were you able to get started from the instructions provided in that other thread, or are you working this exercise in another way?pranzo said:
Please provide specifics. Thank you.
Eliz.
population
I haven't gotten very far at all. I came up with a number of about 50,000 after 156 years, but that doesn't seem right. Neither does 1.2 million after 4 generations according to an earlier reply. I haven't looked at the rat example listed above enough to see how it would help. Do you have any ideas? It should be a simple problem... All I want is 150 years. Each couple (starting at 75 couples) has 1 child a year until they die at 75 years old. Each child will be able to do the same whence they turn 13. Forget how ridiculous that sounds. I'd just like a simple straighforward, but detailed answer. I don't know if my calculations have been correct, but I see 75 new couples every 13 years. After 156 years I got a number around 50,000. I don't know if 190,000 is possible.
I haven't gotten very far at all. I came up with a number of about 50,000 after 156 years, but that doesn't seem right. Neither does 1.2 million after 4 generations according to an earlier reply. I haven't looked at the rat example listed above enough to see how it would help. Do you have any ideas? It should be a simple problem... All I want is 150 years. Each couple (starting at 75 couples) has 1 child a year until they die at 75 years old. Each child will be able to do the same whence they turn 13. Forget how ridiculous that sounds. I'd just like a simple straighforward, but detailed answer. I don't know if my calculations have been correct, but I see 75 new couples every 13 years. After 156 years I got a number around 50,000. I don't know if 190,000 is possible.
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You're just not close.
First generation: 150 people.
These folks have 75 kids in years 13-75. That makes:
Second Generation: 4,725 people
ALL the first and second generation are alive in year 75. Maximum 4,872 people, just counting these two generations.
I'll ignore the odd numbers and put up with partial people.
These folks start to have kids in year 26. The number of 3rd generation folks increases every year. There are more born all the way through year 150. There are 2,362.5 born in year 88 alone.
Third Generation: 148,837.5 individuals
Peak population is now year 101 with a total of 106,650. Remaining population of the first three generations at year 150 is still 57,037.5.
Fourth Generation: By year 150, there have been born of this generation 2,280,731.25
The peak population is now in year 114 - a total of 1,404,131 individuals. Of these four generations, there remain alive at year 150 a total of 1,200,731 individuals.
OK I'm tired of this game. They are not hard to count. It is just awfully tedious. There are EIGHT more generations to go!!!
Again, 190,000 is trivial under these assumptions. Let's throw in some smallpox, or something.
First generation: 150 people.
These folks have 75 kids in years 13-75. That makes:
Second Generation: 4,725 people
ALL the first and second generation are alive in year 75. Maximum 4,872 people, just counting these two generations.
I'll ignore the odd numbers and put up with partial people.
These folks start to have kids in year 26. The number of 3rd generation folks increases every year. There are more born all the way through year 150. There are 2,362.5 born in year 88 alone.
Third Generation: 148,837.5 individuals
Peak population is now year 101 with a total of 106,650. Remaining population of the first three generations at year 150 is still 57,037.5.
Fourth Generation: By year 150, there have been born of this generation 2,280,731.25
The peak population is now in year 114 - a total of 1,404,131 individuals. Of these four generations, there remain alive at year 150 a total of 1,200,731 individuals.
OK I'm tired of this game. They are not hard to count. It is just awfully tedious. There are EIGHT more generations to go!!!
Again, 190,000 is trivial under these assumptions. Let's throw in some smallpox, or something.
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Re: good answer
You appear to have added new requirments to this exercise. Please reply with the full and exact statement of the exercise, the complete instructions, and a clear listing of what you have done. If you have questions, please specify where you are having difficulty.
Thank you.
Eliz.
This almost sounds as though you are the instructor and the tutors are the students, and that you are assigning and grading the tutors' work. But isn't this your assignment? Aren't you supposed to be doing some work on it?pranzo said:
You appear to have added new requirments to this exercise. Please reply with the full and exact statement of the exercise, the complete instructions, and a clear listing of what you have done. If you have questions, please specify where you are having difficulty.
Thank you.
Eliz.
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OK I was bored.
It looks like I was a little off, before, but I had only some generations included. This is all generations. It is a little high, since I didn't adjust for unmatched individuals and I did allow partial people. I seriously doubt that error is greater than 1%.
It is important to note that NONE dies from the last 6 generations by the time year 150 rolls around. None!!
Generation 8, with almost 1 billion births, still has 15 birth years left when year 150 cuts it off.
2.5 billion is substantially more than the trivial 190,000 where we started. This model is in year 69, just starting generation 6, when it crosses 190,000.
Isn't there a Star Trek episode about this sort of thing?
It looks like I was a little off, before, but I had only some generations included. This is all generations. It is a little high, since I didn't adjust for unmatched individuals and I did allow partial people. I seriously doubt that error is greater than 1%.
It is important to note that NONE dies from the last 6 generations by the time year 150 rolls around. None!!
Generation 8, with almost 1 billion births, still has 15 birth years left when year 150 cuts it off.
2.5 billion is substantially more than the trivial 190,000 where we started. This model is in year 69, just starting generation 6, when it crosses 190,000.
Isn't there a Star Trek episode about this sort of thing?