The population of a city Increased from 22,700 to 26,300 between 2004 and 2010. Find the changeof population per year if we assume the change was constant from 2004 and 2010.The population Increased bypeople per year.
Accepted Solution
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Answer:The population increase by people per year at rate of 2.4 %Step-by-step explanation:Given in the question as The Population of city in 2004 was 22,700The population of city in 2010 is 26,300Let the rate of increase of people per year is R%So, population is increase from 2004 to 2010 i.e in 6 yearsSo, equation can be written as Final population = Initial population [tex]( 1+ \frac{Rate}{100})^{6}[/tex]Or, 26,300 = 22,700 [tex]( 1+ \frac{Rate}{100})^{6}[/tex]Or, [tex]\frac{26,300}{22,700}[/tex] = [tex]( 1+ \frac{Rate}{100})^{6}[/tex]Or, 1.158 = [tex]( 1+ \frac{Rate}{100})^{6}[/tex]Or ,[tex](1.158)^{\frac{1}{6}}[/tex] = 1 + [tex]\frac{Rate}{100}[/tex]Or , 1.024 - 1 = [tex]\frac{Rate}{100}[/tex]Or, 0.024 = [tex]\frac{Rate}{100}[/tex]∴ Rate = 0.024 × 100 = 2.4 Hence the population increase by people per year at the rate of 2.4% Answer