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The population of a city in 2005 was 18000. By 2010, the city’s population had grown to 45,000. Economists have determined that the growth is exponential. If they are correct, what is the projected population for 2015?

Respuesta :

first do 45000-18000=27,000 
and approx projected population is 45,000+18000=63,000
your answer is 63,000
apocritia

Solution:

we are given that

The population of a city in 2005 was 18000.

By 2010, the city’s population had grown to 45,000.

Economists have determined that the growth is exponential.

As we know the exponential growth is defined by the relation

[tex]P=p_0e^{rt}\\ \\ \text{where P is the population at time t and initial population is } p_0\\[/tex]

Here we have [tex]p_0=18000, P=45000, t=5[/tex]

substitute these values we get

[tex]45000=18000e^{5r}\\ \\ r=0.183[/tex]

So we get

[tex]P(t)=18000e^{0.183t}[/tex]

So For population is 2015 substitute t=10

[tex]P(10)=18000e^{0.183*10}[/tex]

[tex]P(10)=112209.9598 [/tex]

The projected population for 2015 is 112210

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