The population of Ecuador rose from 9.9 million in 1996 to 15.0 million in 2013.Using the geometric mean, compute the average annual rate of increase over this 17-year period.
A)3.16%
B)5.09%
C)1.56%
D)2.77%
E)2.47%

Question

Quizplus · Accepted Answer

The geometric mean rate of increase, $r$, is found using the formula for growth: $Final = Initial \times (1 + r)^{n}$, where $n$ is the number of periods. Rearranging to solve for $r$, we get $r = \left(\frac{Final}{Initial}\right)^{\frac{1}{n}} - 1$. Plugging in the given values: $r = \left(\frac{15.0}{9.9}\right)^{\frac{1}{17}} - 1$, which approximately equals 0.0247 or 2.47% when converted to a percentage.

The Population of Ecuador Rose from 9