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Math Help - Tree Planting

  1. #1
    Junior Member Godfather's Avatar
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    Tree Planting

    One person owns 7000 trees, and plans to sell 12% of his tree's and plant 600 new ones every year. Will he run out of tree's?(Write a recursive formula that can be used to solve the equation)
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  2. #2
    Junior Member
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    no he will not run out of trees rather he will keep selling only 5000 because 12% of 5000 is 600 so he sells 600 trees and he has 4400 and he plants 600 more and it becomes 5000 well basically it keeps goin on, i think the question is related to limits and this could be the formula where x is the number of trees and not the number of years \frac {88x +60000}{100}
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  3. #3
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    If t_n is a number of trees the guy has after n years, then the initial condition of the recursive formula is

    t_0 = 7000

    and we can see that
    t_1 = 7000 - 0.12*7000 + 600
    or
    t_1 = t_0 - 0.12*t_0 + 600

    For year n we then have
    t_n = 0.88*t_{n-1} + 600
    This is your recursive formula.

    To find out whether he will run out of trees solve this relation and take it's limit when n approaches infinity.

    Update:
    Made some corrections in the formula.
    Last edited by kooker; December 17th 2008 at 07:44 PM.
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