Multiple choice

Population of a city 'X' is 100 and it increases by 50% per year, and initial production of the food in village 'X' is 100 tonnes and it increases by 100 tonnes a year. If each person requires at least 1 tonne of food per year and food stock is exhausted every year, then after how long would the food production in the city be insufficient for the entire population? (Assume that they cannot import food from anywhere)

  1. 2 years

  2. 3 years

  3. 4 years

  4. 7 years

  5. Never
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Population P(n) = 100 * (1.5)^n. Food F(n) = 100 + 100n. We need to find n such that F(n) < P(n). For n=3: F=400, P=100*3.375=337.5. For n=4: F=500, P=100*5.0625=506.25. Since 500 < 506.25, the food is insufficient after 4 years.

AI explanation

By evaluating the population and food supply year by year, we start at year 0 with 100 people and 100 tonnes. After 1 year, the population is 150 and the food supply is 200 tonnes; after 2 years, the population is 225 and the food is 300 tonnes; after 3 years, the population is 337.5 and the food is 400 tonnes. In the 4th year, the population becomes 506.25, while the food supply only increases to 500 tonnes, meaning the food production is no longer sufficient. The result is 4 years.

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