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Model for a popluation growth

  1. Dec 11, 2007 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data
    In a model for the growth of a population,[itex]p_n[/itex] is the number of individuals in the population at the end of n years. Initially, the population consists of 1000 individuals.

    In each year, the population increases by 20% and on Dec.31st, 100 individuals leave the population.

    a)Calculate [itex]p_1 \ and \ p_2[/itex]
    b)Write down an equation connecting [itex]p_{n+1} \ and \ p_n[/itex]
    2. Relevant equations

    None

    3. The attempt at a solution

    Well at the initial time. p=1000

    so at the end of the first year it would just be 1000-100
    so that [itex]p_1=900[/itex]

    At the start of the next year the new population size is [itex]\frac{120}{100}*900=1080[/itex]
    so then simply [itex]p_2=1080-100=980[/itex]

    are these values correct?
    If my answers are correct, then for part b) should it just simply be
    [tex]p_{n+1}=(1.2*p_n)-100[/tex]
     
  2. jcsd
  3. Dec 11, 2007 #2

    Dick

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    I think you want to grow the population by 20% first, then subtract 100. As you wrote in b), but didn't do in a).
     
  4. Dec 11, 2007 #3

    rock.freak667

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    But in part a) doesnt initially mean that it is at the start of the calender year and the population growth should be valid for the year after?
     
  5. Dec 11, 2007 #4

    Dick

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    I would say Dec 31 is at the end of the year, so you would start with 1000 on Jan 1 of the first year. I was just trying to make b) applicable to p0=1000. It's roughly the same problem either way, in one case you start with 1000 on Dec 31, in the other with 1000 on Jan 1.
     
  6. Dec 11, 2007 #5

    rock.freak667

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    so then the formula for P_n and P_n+1 is correct?
     
  7. Dec 12, 2007 #6

    HallsofIvy

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    Yes, it is.
     
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