Question

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

Answer 1

The exponential growth formular is given by
$P=P_o(r)^t$
where: P is the population of the country, t years after the initial year (i.e. in this case, 1994).
$P_o$ 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, $P_o=140$, and t = 4 years

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

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
$140(1.010546)^{17}=140(1.195236)=167.33$ million

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