Question

The number of Internet users in Mexico between 2004 and 2008 can be modeled as u(t) = 8.02(1.17^t) million users where t is the number of years since 2004.
(a) On average, what was the rate of change in the number of Internet users in Mexico between 2004 and 2008? (Round your answer to three decimal places.) million users per year
(b) What was the percentage change in the number of Internet users in Mexico between 2004 and 2008? (Round your answer to three decimal places.)
(c) The population of Mexico in 2008 was 109,955,400. What percentage of the Mexican population used the Internet in 2008? (Round your answer to three decimal places.)

Answer 1

Question (a):

For this case we have the following function:

$u (t) = 8.02 (1.17 ^ t)$

We must find the rate of change in the number of Internet users.

For this, we use the following equation:

$AVR = \frac {u (t2) -u (t1)} {t2-t1}$

• For $t2 = 4$ we have:

$u (4) = 8.02 (1.17 ^ 4)\\u (4) = 15.03$

• For $t1 = 0$ we have:

$u (0) = 8.02 (1.17 ^ 0)\\u (0) = 8.02$

Substituting values ​​we have:

$AVR = \frac {15.03-8.02} {4-0}\\AVR = 1.753$

Answer:

he rate of change in the number of Internet users in Mexico between 2004 and 2008 is:

$AVR = 1.753\ million\ users\ per\ year$

Question (b):

• For the year 2004 we have:

$u (0) = 8.02 (1.17 ^ 0)\\u (0) = 8.02$

• For the year 2008 we have:

$u (4) = 8.02 (1.17 ^ 4)\\u (4) = 15.03$

Therefore, the percentage change is:

$\% Change = (\frac {final\ value - initial\ value} {initial\ value}) * 100$

Substituting values:

$\% Change = (\frac {15.03 - 8.02} {8.02}) * 100\\\% Change = 87.406%$

Answer:

 the percentage change in the number of Internet users in Mexico between 2004 and 2008 is:

$\% Change = 87.406\%$

Question (c):

For this case we have that the total population in Mexico for 2008, is given by:

109,955,400

The number of internet users for 2008 is:

15,030,000

Therefore, the percentage of the population that uses the internet in Mexico for 2008 is given by:

$\% = (\frac {Partial\ value} {Total\ value}) * 100$

Substituting values ​​we have:

$\% = (\frac {15,030,000} {109,955,400}) * 100\\\% = 13.669\%$

Answer:

The Mexican population used the Internet in 2008 is:

$\% = 13.669\%$