1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Financial mathematics-recurrence relations

  1. Nov 8, 2012 #1
    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?

    3. The attempt at a solution
  2. jcsd
  3. Nov 8, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    First: please write the recurrence correctly. What you have written means
    [tex] x_n = 0.95 x_n - 1 + N,[/tex] but maybe you really mean
    [tex] x_n = 0.95 x_{n-1} + N.[/tex] If that is the case, use parentheses:
    x_n = 0.95 x_(n-1) + N.

    Anyway, What is x_0 (assuming time 0 is the beginning of the first year). What is x_1? (Just write it down in detail). Then, what is x_2? Continue for one or two more steps until you see the pattern.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook