Differential Equations 3 Question 12
12. A country has food deficit of . Its population grows continuously at a rate of per year. Its annual food production every year is 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 years, where is the smallest integer bigger than or equal to .
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Answer:
Correct Answer: 12.
Solution:
- Let
be initial population of the country and be its initial food production. Let the average consumption be unit. Therefore, food required initially . It is given
Let
Then,
Let
Then,
Food consumption in the year
Again,
[given]
Taking log on both sides, we get
Thus, the least integral values of the year