SOLUTION: Good Morning all, Use of the internet in a country is given by the function f(x)=0.485x^2 - 1.694x + 0.315, where the output is in millions of users. In this formula x=6 corresp

Question 460148: Good Morning all,
Use of the internet in a country is given by the function f(x)=0.485x^2 - 1.694x + 0.315, where the output is in millions of users. In this formula x=6 corresponds to 1996, x=7 corresponds to 1997, and so on until x=20 corresponds to 2010.
Estimate when the number of internet users in the country reached 144 million?
What year?
Thank you in advance.
Minka
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Use of the internet in a country is given by the function f(x)=0.485x^2 - 1.694x + 0.315, where the output is in millions of users. In this formula x=6 corresponds to 1996, x=7 corresponds to 1997, and so on until x=20 corresponds to 2010.
Estimate when the number of internet users in the country reached 144 million?
Given:
f(x)=0.485x^2 - 1.694x + 0.315
Set f(x) to 144 and solve for x:
144 = 0.485x^2 - 1.694x + 0.315
0 = 0.485x^2 - 1.694x - 143.685
applying the quadratic formula, we get:
x = {19.05, -15.55}
we can toss out the negative solution leaving:
x = 19 (years from 1990
.
calculating the year:
1990+ 19 = 2009
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=281.618536 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 19.0469008812773, -15.5541173761227. Here's your graph:

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