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Math Help - rabbit population

  1. #1
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    rabbit population

    If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.
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    I would use the following population model. There are others you could consider

    P = P_0R^t

    where P = population, P_0 = Initial Population, R = Growth Rate and t = time in years

    In your case

    P_0 = 15,000, R = 3% (increasing) and t = 15

    therefore P = 15,000(1.03)^{15}

    you should be fine from here...
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  3. #3
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    Quote Originally Posted by pickslides View Post
    I would use the following population model. There are others you could consider
    Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?
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  4. #4
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    Quote Originally Posted by Joker37 View Post
    If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.
    Quote Originally Posted by Joker37 View Post
    Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?
    15,000 + 3% of 15,000 = 15,000 + (0.03)(15,000) = 15,000 + 540 = 15,450.

    15,450 + 3% of 15,450 = 15,450 + (0.03)(15,450) = 15,450 + 463.5 = 15,913.5

    etc etc.
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  5. #5
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    You have to think like if you where figuring out saving account interest.
    15000____100%
    ?????_____3%

    15000 times 3% divide it by 100

    45000 divide by 100 = 450

    At the end of the first year you have 15450 rabbits. then 15450 is your new 100% and you start all over until 15 years have pass.
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  6. #6
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    Quote Originally Posted by Joker37 View Post
    Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?
    I think the model I have given you is probably the most easiest to understand. My advice would be to get your head around this one first of all and then look into exploring more complex models.
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  7. #7
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    Quote Originally Posted by Joker37 View Post
    If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.
    I learnt mine as P=P_0(1+x)^t which is in essence the same as pickslides' method except he has R where I have (1+x).

    The exponential model is probably the simplest method.

    Of course this is based on the assumption that the growth can be modelled by exponential growth and that there are no reasons for numbers to decline
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