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The population of a city in 2005 was 18,000. By 2010, the city’s population had grown to 45,000. Economists have determined that the population growth follows an exponential model. If they are correct, what is the projected population for 2015?

Respuesta :

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Figure out the exponential model by finding 1 + r:

45000 = 18000(1+r)^5

Divide both sides by 18000

(1+r)^5 = 2.5

Take the fifth root of each side:

[tex]1 + r = \sqrt[5]{2.5} [/tex]

therefore the model is:
[tex]P = 18000( \sqrt[5]{2.5} )^{t} [/tex]
where t is the years after 2005

So to find 2015:

[tex]P = 18000( \sqrt[5]{2.5} )^{10} [/tex]
P = 112,500

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