Jee mains 2000 maths food deficit 10%

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 (ln 10 - ln 9)/ (ln ( 1.04 ) - 0.03).

Solution:
Key point to note here is that population is growing continuously whereas food production is growing annually.

So
P_n = P_0.e^(rt)
F_n = F_0.(1 + r/100)^t

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