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Math Help - financial mathematics-recurrence relations

  1. #1
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    financial mathematics-recurrence relations

    A person has inherited a surplus grain mountain of 30000 tonnes held in a warehouse.each year 5% of the grain is eaten by mice.The person is obliged to add N tonnes each year.find the maximum of N such that mountain will decrease in size.


    This is what I have understood the problem.

    Initial amount=30000 Tonnes
    Each year 5% loss implies remaining amount is 95%.
    N tonnes is added each yer.

    So I can form the recurrence relation as x_n=0.95 x_n-1+N

    But how an I find the maximum of N?
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  2. #2
    MHF Contributor
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    Re: financial mathematics-recurrence relations

    Hey chath.

    If something is decreasing then eventually x_n will be zero for some value of positive n.

    Can you re-write this equation in explicit form and find the condition for N such that it equals zero for any value of fixed n?

    I took this course a very long time ago so if you have formulas for the course please share them.
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