Question

the table gives the number of cellular telephone subscribers in a country (in thousands) from 2005 through 2010. find the average annual rate of change during this time period.

year	subscribers (in thousands)
2006	279,935
2007	291,762
2008	318,369
2009	319,264
2010	324,805

the average annual rate of change during the time period 2005 - 2010 is
(round to the nearest unit as needed.)

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change over a time period from \( t_1 \) to \( t_2 \) is \(\frac{f(t_2)-f(t_1)}{t_2 - t_1}\), where \( f(t) \) is the function representing the quantity (here, number of subscribers) at time \( t \).

Here, \( t_1 = 2005 \), \( f(t_1)=270149 \) (subscribers in thousands), \( t_2 = 2010 \), \( f(t_2)=324805 \) (subscribers in thousands). The time difference \( t_2 - t_1=2010 - 2005 = 5 \) years.

Step2: Calculate the change in subscribers

First, find the difference in the number of subscribers: \( f(t_2)-f(t_1)=324805 - 270149 \).
\( 324805-270149 = 54656 \).

Step3: Calculate the average annual rate of change

Now, divide the change in subscribers by the number of years: \(\frac{54656}{5}\).
\(\frac{54656}{5}=10931.2\). Rounding to the nearest unit, we get \( 10931 \).

Answer:

10931