Velkrowmonster
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A country's population in 1994 was 140 million. n 1998 it was 146 million. Estimate the population in 2011 using the exponential growth formula. Round your answer to the nearest million

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nobillionaireNobley
The exponential growth formular is given by
[tex]P=P_o(r)^t[/tex]
where: P is the population of the country, t years after the initial year (i.e. in this case, 1994).
[tex]P_o[/tex] is the initial population of the country (i.e. the population of the country in 1994).
r is the growth rate of the population and
t s the number of years after the initial year.

We obtain the value of r by comparing the growth between 1994 and 1998.
Here: P = 146, [tex]P_o=140[/tex], and t = 4 years

Thus
[tex]146=140(r)^4 \\ \\ r^4= \frac{146}{140} =1.042857 \\ \\ r= \sqrt[4]{1.042857} =1.010546[/tex]

To estimate the population of the country in 2011, we note that 2011 is 17 years after 1994.

Thus, the population of the country in 2011 can be estimated to be
[tex]140(1.010546)^{17}=140(1.195236)=167.33[/tex] million

Therefore, the population of the country in 2011 can be estimated to be 167 million to the nearest million.

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