Respuesta :
Question (a):
For this case we have the following function:
[tex]u (t) = 8.02 (1.17 ^ t)[/tex]
We must find the rate of change in the number of Internet users.
For this, we use the following equation:
[tex]AVR = \frac {u (t2) -u (t1)} {t2-t1}[/tex]
- For [tex]t2 = 4[/tex] we have:
[tex]u (4) = 8.02 (1.17 ^ 4)\\u (4) = 15.03[/tex]
- For [tex]t1 = 0[/tex] we have:
[tex]u (0) = 8.02 (1.17 ^ 0)\\u (0) = 8.02[/tex]
Substituting values we have:
[tex]AVR = \frac {15.03-8.02} {4-0}\\AVR = 1.753[/tex]
Answer:
he rate of change in the number of Internet users in Mexico between 2004 and 2008 is:
[tex]AVR = 1.753\ million\ users\ per\ year[/tex]
Question (b):
- For the year 2004 we have:
[tex]u (0) = 8.02 (1.17 ^ 0)\\u (0) = 8.02[/tex]
- For the year 2008 we have:
[tex]u (4) = 8.02 (1.17 ^ 4)\\u (4) = 15.03[/tex]
Therefore, the percentage change is:
[tex]\% Change = (\frac {final\ value - initial\ value} {initial\ value}) * 100[/tex]
Substituting values:
[tex]\% Change = (\frac {15.03 - 8.02} {8.02}) * 100\\\% Change = 87.406%[/tex]
Answer:
the percentage change in the number of Internet users in Mexico between 2004 and 2008 is:
[tex]\% Change = 87.406\%[/tex]
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:
[tex]\% = (\frac {Partial\ value} {Total\ value}) * 100[/tex]
Substituting values we have:
[tex]\% = (\frac {15,030,000} {109,955,400}) * 100\\\% = 13.669\%[/tex]
Answer:
The Mexican population used the Internet in 2008 is:
[tex]\% = 13.669\%[/tex]
The average rate of change in the number of internet users in Mexico between 2004 and 2006 was 1.479 million.
The percentage change in the number of internet users between 2004 and 2006 was 36.89%.
13.668% of the population was internet users in 2008 in Mexico.
Given
The number of internet users in Mexico between 2004 and 2008 is modeled by the following equation:
[tex]\rm u(t) = 8.02(1.17^t)[/tex]
Where u(t) is in millions and t is the number of years since 2004.
Rate of change of internet users between 2004 and 2006;
1. The rate of change of a function is defined as:
[tex]\rm Rate \ of \ change =\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
We have to find the rate of change between 2004 and 2006.
For 2004 t = 0, and for 2006, t = 2.
So the rate of change for the given function will be:
[tex]\rm Rate \ of \ change =\dfrac{u(2)-u(0)}{2-0}\\\\Rate \ of \ change =\dfrac{8.02(1.17)^2-8.02(1.17)^0}{2}\\\\Rate \ of \ change =1.479[/tex]
The average rate of change in the number of internet users in Mexico between 2004 and 2006 was 1.479 million.
2. Percentage change of internet users between 2004 and 2006.
The formula to calculate the percentage change is:
[tex]\rm Percentage =\dfrac{New \ value -Original \ value}{Original \ value}\times 100[/tex]
Here, the new value means the users in 2006 and the original value means the users in 2004.
Using the values in this formula, we get:
[tex]\rm Percentage =\dfrac{New \ value -Original \ value}{Original \ value}\times 100\\\\\rm Percentage =\dfrac{8.02(1.17)^2-8.02(1.17)^0}{8.02(1.17)^0}\times 100\\\\ Percentage =36.89 \ percent[/tex]
The percentage change in the number of internet users between 2004 and 2006 was 36.89%.
3. Percentage of internet users in 2008
For 2008, t would be equal to 4.
So, the number of internet users in Mexico in 2008 would be;
[tex]\rm = {8.02(1.17)^4}\\\\=15.02 \ milion[/tex]
Total population of Mexico in 2008 = 109,955,400
We have to calculate what percentage of Mexico's population was Internet users in 2008. '
The formula for this would be:
[tex]\rm = \dfrac{Concerned \ value}{Total \ value}\times 100[/tex]
Here, the concerned value is the number of internet users and the total value is the total population.
Using the values in this formula we get:
[tex]\rm = \dfrac{Concerned \ value}{Total \ value}\times 100\\\\\rm = \dfrac{ 15,028,575}{109,955,400}\times 100\\\\= 13.66 \ percent[/tex]
Thus, 13.668% of the population was internet users in 2008 in Mexico.
To know more about rate of change click the link given below.
https://brainly.com/question/18849239
