According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?

Question

Evangeline Preston

Mathematics

30 September, 04:22

According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?

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Answers (1)

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Julianna Cabrera · Answer 1

Firstly, the rate of increase of Canton = 80/7720 = 0.010

The rate of increase of HP = 120/3200 = 0.0375

Apply the formula of compound interest==> A = A' (1+i) ^n

The population will be equal when the following equality is satisfied

7720 (1+0.01) ^n = 3200 (1+0.0375) ^n

or

7720x1.01^n = 3200x1.0375^n

Divide both sides by 3200 = = = > (193/80) x1.01^n=1.0375^n