Complicated maths question

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1

Starting with one woman, who gives birth to twin daughters every year from the age of 25 to 50, and then dies, followed by exactly the same thing happening to all of her offspring, and all of their offspring, and so on, ad infinitum, how does one calculate the size of the female population in any given year (expressed, for simplicity, in years after the birth of the first woman)?

And in any given year, what proportion of the female population will be what age? I’m assuming that these proportions will remain constant, though I may be wrong.

2

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It’s been fun thinking/doodling the maths for this, so far.

3

It’s a bit tricky.

4

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Well… I can think the process in my head, but doing the maths for it is in a whole other ballpark altogether.

5

“Well this one is tricky.”

  • Wonder Woman
6

Every 25 years the female population increases by 50 = 25 sets of twins.

So when the first woman dies, there will be 50 daughters after 25 years.

When those 50 daughters die, they will have had 2,500 granddaughters after 50 years.

When those 2,500 granddaughters die, they will have had 125,500 great-granddaughters after 75 years.

When those 125,000 die, they will have had 6,250,000.

50^x, where x = 25 year intervals

There’s more algebra involved, like subtracting deaths, to solve each individual year but at least this is a start.

7

Yes, that’s true, but the births are staggered, and this will have a knock on effect with each generation.

8

My response was a freebee, anymore work and I need compensation to be your math tutor. Good luck!

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That’s right… the formula has to allow for all females, having 2 children per year, when the first set of twins hit 25… then the 2nd set the following year… the 3rd set the year after that… ad infinitum.

But I agree with urwrong, in that the resultant formula necessitating compensation… coz this necessitates, a whole lotta thinking. In having started on the formula, the maths gets interesting/needs accommodating the data, once the first set of twins hits 25.

10

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I’ve just pictured a [new] way to express it… because it’s the expression part of the solution of the mathematical inquiry, that is key to resolving this.

11

Would it be easier if we just said one daughter per year, that is, 25 daughters in 25 years? I suppose that would just be a case of changing one specific quantity in the formula, and wouldn’t make much difference to the mechanics of it.

12

There’s two daughters every year because they’re twins.

I would just chart the first 50 years or so and see the pattern that way. Each female has a linear growth of 50 progeny. But the amount of those progeny reaching age 25 is exponential, because massive amounts of women start becoming fertile over time. Then you have to subtract the mother after she dies, so minus one.

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@ Maia: That doesn’t matter at this juncture… though it would make the representation clearer to follow/interpret.

14

Year one = 1 woman
Year two = 1 woman
Year three = 1 woman
…
Year twenty-five = 3 women (1 mother + 2 daughters)
Year twenty-six = 5 women (1 mother + 2 + 2 daughters)
Year twenty-seven = 7 women (1 mother + 2 + 2 + 2 daughters)
…
Year fifty = 50 women (2 new mothers = +4 daughters)
Year fifty-one = 54 women (2 mothers + 4 daughters + 2 new mothers + 4 new daughters)
Year fifty-two = 62 women (4 mothers + 8 daughters + 2 new mothers + 4 new daughters)
Year fifty-three = 78 women (6 mothers + 12 daughters + 2 new mothers + 4 new daughters)

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.and that needs one hell of a formula, to encompass and express the yearly ever-changing quantity… post the first 25 years, of course.

I started an equation, for it… was fun to try compile, I must say.

16

it’s all females in the end

why overcomplicate this with symbols other than the ones we normally use (words)?

not that “all females” would be complicated to express if you speak that lingo

17

Sorry I just actually read it. lol

So it increases x^2 every year, and every birth is from an individual that is <1yr of age, or whole population (however whole is expressed in proportion/ratio/percentage)… 2x, 1:1, 1::1? I dunno.

18

isn’t it, like, weird how you have to cube it (3) to get to 4 cuz they start from zero? 4D, I mean. how weird is it that you can start from zero and get somewhere?

maybe…

maybe you don’t start from zero

“there is no zero”

sorry. please pardon this tangent.

19

It’s not x^2 because there’s a delay between when the daughters become mothers. They have to wait 25 years, by that time, there are other generations producing which complicates the exponential growth.

Furthermore, each woman gives birth to 50 daughters after 25 years (twins each year). So that is also not to the second power.

20

wow my brain skipped past the 25-50 part…

i’m so glad things don’t actually work that way