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Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened
in 1990, the population of Marymount increased by about 20% each year for the first ten years and then increased by
5% each year after that.
a. If the population was 150,000 people in 2010, what was the population in 2000?
b. How should you round your answer? Explain.
c. What was the population in 1990?
If the trend continued, what would the population be in 2009??

Respuesta :

Answer:

92087,14873

Step-by-step explanation:

Given that Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened  in 1990, the population of Marymount increased by about 20% each year for the first ten years and then increased by  5% each year after that

Let P0 be the population in 1990

Then we have in 2000 the population is

[tex]P(2000) = P_0(1.2)^{10}[/tex]

with this initial population for next growth we have in 2010 the population would be

[tex]P(1.05)^{10}[/tex], where P = population is 2000

a) Given that [tex]P(1.05)^{10) = 150000\\P = 150000(1.05)^{-10} =92.086.99\\=92087[/tex]

b) we use the exponential equation and solve for initial population in 2000.

c) we have

[tex]P_0(1.2)^{10} =92087\\P_0 = 92087((1.2)^{-10})\\=14872.56\\=14873[/tex]

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