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I want to know how to calculate following

We have one female that gives birth to one child every year for 10 years. Out of 10 children 5 are female and after 20 years they can reproduce as well. How could I calculate total population after specified time and with different starting number.

I am not math student and I haven't had any math classes in long time, if somebody can please show me how can I calculate things like this.

Thanks

user3256672
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  • what's the average age of death ? that would play in on long enough time scales. –  Sep 13 '17 at 14:03
  • I don't need to add death to calculation, but one can only reproduce for 10 years – user3256672 Sep 13 '17 at 14:09
  • well you do to some extent because unless someone never passes away that will affect the result some. also are they reproducing on their own or is there also a first man etc. –  Sep 13 '17 at 14:11
  • to show why if 20 generations of (two reproducers per previous reproducer only ) are born without death and one only birth, then 2^21-1 or roughly 2.1 million people exist at the end of the 21st generation if you only say 3 generations are left then that falls to under 1.9 million. –  Sep 13 '17 at 14:21
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    @RoddyMacPhee. I guess the OP wants to count the dead ones too. – uniquesolution Sep 13 '17 at 14:24
  • @RoddyMacPhee you are correct! I forgot about that. The life expected is 60 years. – user3256672 Sep 13 '17 at 14:33
  • Also they are reproducing on their own but only half of offspring are female and can reproduce. – user3256672 Sep 13 '17 at 15:31
  • Without being helpful in any way, I'll point out this appears to be a recursive relation very similar to the Fibonacci numbers. –  Sep 13 '17 at 15:45

1 Answers1

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okay so the original few generations look like this:

  • 1
  • 10
  • 50
  • 250
  • 1250

so this ( other than the original one) is $10\cdot 5^{n-1}$ in generation n ( assuming the 1 is generation 0). Now you say they last 60 years, each generation is produced in 20, that makes three generations, so what is $10\cdot 5^{n-1}+10\cdot 5^n+10\cdot 5^{n+1}$ that's 10 times the sum of the powers of 5 involved or 10 times the sum of a finite geometric series ( admittedly I can't remember the formula for solving that sum right now). at that point you can solve for the population at any time after the first 60 years.

  • In this calculation is 5 number of children that can reproduce? Is male population included? – user3256672 Sep 15 '17 at 12:29
  • each of the 5 reproducers in the 10 generation produce 10 giving 50 each of the 25 reproducers in that generation produce 10 making 250 each of the 125 reproducers in that generation produce 10 which gives 1250. –  Sep 15 '17 at 12:41