A country has a food deficit of `10%`. Its population grows continuously at a rate of `3%` per year. Its annual food production every year is 4% more than that of the last year. Assuming that the average food requirement per person remains constant, prove that the country will become self-sufficient in food after `n` years, where `n` is the smallest integer bigger than or equal to `(ln10-ln9)/(ln(1.04)-0.03)`

Explanation

To solve the problem, we need to analyze the population growth and food production of the country over time. We will derive the necessary expressions and inequalities to find the smallest integer \( n \) such that the country becomes self-sufficient in food.

### Step 1: Define Variables
Let:
- \( x_0 \) = initial population of the country
- \( y_0 \) = initial food production
- \( k \) = food requirement per person

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