Population vs food supply

The population of a country is initially 2.5 million people and is increasing by 0.8 million people every year. The country’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate for an additional 0.4 million people per year.

a. Based on these assumptions, in approximately how many years will the country first experience shortages of food?

b. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.

c. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.

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Solution
a). let x be number of years

Current population is 2.5+0.8x where x is 0

Currently supply is 4+0.4x where x= 0

2.5+0.8x=4+0.4x

0.8x-0.4x=4-2.5

0.4x=1.5

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