The towns of Franklin and Chester each decided in the same year to begin posting their populations on signs by the main entrances into the towns. Each year, they update the signs. Franklin had a population of 20,000 people in the first year that they posted the sign, and each year, the population increases by approximately 5%. Chester had a population of 25,000 people in the first year that they posted the sign, and each year, the population increases by 500 people. In which year will Franklin's population first exceed Chester's population?

Question

Daniela James

Mathematics

22 November, 16:48

The towns of Franklin and Chester each decided in the same year to begin posting their populations on signs by the main entrances into the towns. Each year, they update the signs. Franklin had a population of 20,000 people in the first year that they posted the sign, and each year, the population increases by approximately 5%. Chester had a population of 25,000 people in the first year that they posted the sign, and each year, the population increases by 500 people. In which year will Franklin's population first exceed Chester's population?

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Answers (1)

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Andre Wilkins · Answer 1

In the 8th year, the population of Franklin will exceed Chester.

We have two equations in this problem.

y = 20000 (1.05) ^x

y = 25000 + 500x

There are a few options to determine the answer.

1) Create a chart for each city.

2) Use a graphing calculator to graph them.

3) Solve the equation to determine when they are equal.

With any option, you will see they are equal between years 7 and 8. Then, Franklin goes ahead in year 8.