# Financial mathematics-recurrence relations

1. Nov 8, 2012

### 99butterfly

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. Nov 8, 2012

### Ray Vickson

First: please write the recurrence correctly. What you have written means
$$x_n = 0.95 x_n - 1 + N,$$ but maybe you really mean
$$x_n = 0.95 x_{n-1} + N.$$ 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.

RGV