financial mathematics-recurrence relations

Oct 2012
sri lanka
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?


MHF Helper
Sep 2012
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.