8. A country has 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 (In $\mathbf { 1 0 } - \mathbf { I n } \mathbf { 9 } ) / ( \mathbf { I n } ( \mathbf { 1 . 0 4 } ) - \mathbf { 0 . 0 3 } )$.