Question

The number of internet users in mexico between 2004 and 2008 can be modeled as u(t) = 8.02(1.17t) million users where t is the number of years since 2004

Answer 1

a) 1.479 Million

b) 36.9%

c) 13.668%

Explanation:

The complete question is attached in the image below.

The number of internet users in Mexico between 2004 and 2008 is modelled by the following equation:

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

Where, u(t) is in millions and t is the number of years since 2004.

Part a) Rate of change of internet users between 2004 and 2006

The rate of change of a function is defined as:

`(f(x_(2))-f(x_(1)))/(x_(2)-x_(1))`

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:

`(u(2)-u(0))/(2-0)\\\\ =(8.02(1.17)^(2)-8.02(1.17)^(0))/(2)\\\\ =1.479`

Thus, the average rate of change in number of internet users in Mexico from between 2004 and 2006 was 1.479 million.

Part b) Percentage change of internet users between 2004 and 2006

The formula to calculate the percentage change is:

`\frac{\text{New value - Original Value}}{\text{Original Value}} * 100\%`

Here, New value means the users in 2006 and original value means the users in 2004.

Using the values in this formula, we get:

`(8.02(1.17)^(2)-8.02(1.17)^0)/(8.02(1.17)^(0)) * 100\%\\\\  =36.89\%`

Thus, the percentage change in the number of internet users between 2004 and 2006 was 36.89%

Part c) 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 =
`8.02(1.17)^(4)=15.02857542` million = 15,028,575 (rounded to nearest integer)

Total population of Mexico in 2008 = 109,955,400

We have to calculate what percentage of Mexico population was Internet users in 2008. The formula for this would be:

`\frac{\text{Concerned Value}}{\text{Total Value}} * 100\%`

Here, concerned value is the number of internet users and total value is the total population. Using the values in this formula we get:

`(15028575)/(109955400) * 100\%\\\\=13.668\%`

Thus, 13.668% of the population was internet users in 2008 in Mexico.