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2.1.4: Solving Exponential Equations
Two schools opened in the same year, each with a population of 500 students. Hillsboro High School’s population increased at a rate of 160 students per year. The population of Mountain Ridge High School increased by approximately 20% each year.
1. On the tenth anniversary of the schools’ opening, which school has the greater population?
2. How many more students does the school with the larger population have?
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1. On the tenth anniversary of the schools’ opening, which school has the greater population?• Create an expression to represent the population
growth for each school.• Hillsboro High School started with a population of 500
that increased by 160 students each year. This situation can be modeled by the expression 500 + 160n, where n represents the number of years after the school opened. To find the population after 10 years, substitute 10 for n and evaluate the expression.
• Hillsboro High School has 2,100 students after 10 years.
2.1.4: Solving Exponential Equations
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= 500 + 160(10) = 2100500 + 160n
• Mountain Ridge High School also started with a population of 500, but the population increased by 20% each year. This situation can be modeled by the expression 500(1 + 0.20)n, where n represents the number of years after the school opened. To find the population after 10 years, substitute 10 for n and evaluate the expression.
• Mountain Ridge High School has approximately 3,096 students after 10 years.
• After 10 years, Mountain Ridge High School has more students than Hillsboro High School.
2.1.4: Solving Exponential Equations
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= 500(1 + 0.20)10 = 500(1.20)10500(1 + 0.20)n
2. How many more students does the school with the larger population have?• To find the difference in the populations of the two
schools, subtract their populations after 10 years.
3096 – 2100 = 996• After 10 years, Mountain Ridge High School has
approximately 996 more students than Hillsboro High School.
2.1.4: Solving Exponential Equations
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