Question

# A country's birth rate is the number of births per year per $$1000$$ people in the country, and a country's death rate is the number of deaths per year per $$1000$$ people. Immigration refers to the number of people who move into a country each year, and emigration refers to the number of people who move out of the country each year. A country's population growth is determined by these four variables. Table $$1$$ gives birth, death, immigration and emigration rates in four countries and lines $$1-4$$ in Figure $$1$$ model in the population for the four countries shown over time.   Birth Death Immigration EmigrationEast Zealand$$20$$$$x$$$$1000$$$$1000$$West Zealand$$21$$$$21$$$$12100$$$$y$$South Zealand$$36$$$$24$$$$z$$$$500$$North Zealand$$13$$$$13$$$$82000$$$$9600$$Name the country whose population is represented by line $$1$$.

A
East Zealand
B
West Zealand
C
North Zealand
D
South Zealand

Solution

## The correct option is C South Zealand$$\Rightarrow$$  Line $$1$$ shows exponential growth, because the line curves upward. $$\Rightarrow$$  Since, birth rate and death rate are per $$1,000$$ people, a birth rate higher than a death rate will result in exponential growth (because births-deaths will increase as the population increases). $$\Rightarrow$$  Immigration and emigration numbers are per year and therefore have a linear effect on the graph (as the absolute change in the population due to immigration-emigration is constant). $$\Rightarrow$$  South Zealand has more births per $$1,000$$ than deaths per $$1,000$$. $$\therefore$$  Correct answer is option $$D$$ South Zealand.Mathematics

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