A country has a food deficit of 10%. Its population grows continuously at the 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 `(log_e 10-log_e 9)/((log_e 1.04)-0.03)`

Explanation

To solve the problem, we need to analyze the conditions under which the country becomes self-sufficient in food. Let's break down the solution step by step.

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

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