Question

The number of Internet users in Latin America grew from 25.8 million in 2009 to 70.6 million in 2016. Use the geometric mean to find the annual growth rate. (Round your answer to 2 decimal places.)

Answer 1

Answer:

the annual growth rate is 15.47 %

Step-by-step explanation:

Given the data in the question;

Internet users grew from 25.8 million to 70.6 million,

from the year 2009 to the year 2016.

Using geometric mean, Annual growth rate = ?

To determine the average growth rate of a time series using geometric mean, we use the following formula;

$r_{geo$ = [ $($ Xₙ / X₀ $)^{\frac{1}{n}$ ] - 1

where Xₙ is the data value of the last year { 70.6 million }

X₀ is the data value for the first year { 25.8 million }

n is the sample size or the time difference, ( 2016 - 2009 = 7 )

so we substitute;

$r_{geo$ =  [ $($ 70.6 / 25.8  $)^{\frac{1}{7}$ ] - 1

$r_{geo$ = [ $($ 2.736434  $)^{\frac{1}{7}$ ] - 1

$r_{geo$ = [ 1.15466 ] - 1

$r_{geo$ = 0.15466

$r_{geo$ = ( 0.15466 × 100 )%

$r_{geo$ = 15.47 %

Therefore, the annual growth rate is 15.47 %