SOLUTION: 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 z=6 corresponds to 1996-x=20 which

Question 554457: 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 z=6 corresponds to 1996-x=20 which corresponds to 2010. Estimate when the number of Internet uses in the country reached 150 million.
Since the function contains decimal coefficients, we have decided to solve this problem by graphing. To determine when the number of uses reach 150 million, find the x-value of the point where the functions g(x)-18 and f(x)-0.485x^2-1.694x+0.315 intersect.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f(x) = .485x^2 - 1.694x + .315.
output is in millions of users.
i don't understand what you mean by when z = 6 and g(18).
i graphed the function to see what was happening.
here's what the graph looks like.

did you mean when z = 6 corresponds to 1996 - 6 + 20 = 2010?
did you mean x?
i think you must have.
you could have simplified it by saying that the year is 2004 when x = 0
then, when x = 6, the year would be 2004 + 6 = 2010.
at least i think that's what you meant.
if the output is in millions of user, then the y = 150 would equate to 150 million users.
you would need to find the value of x for when y = 150.
per the graph, this would occur somewhere around the point where x = 19.
that looks to be somewhere around when x = 18 that you mentioned.
that would not be g(x) = 18.
that would be x = 18
when x = 18, the value of y = 126.963
to solve for when y = 150, you need to solve the equation of:
.485x^2 - 1.694x + .315 = 150
the easiest way to solve this is to subtract 150 from both sides of the equation to get:
.485x^2 - 1.694x - 149.685 = 0
you would then use the quadratic formula to get the answer.
that answer would be:
x = -15.90803 or x = 19.400818
since x can't be negative, the answer is 150 million users when x = 19.400818.
year 19 equates to the year 2004 + 19 = 2023.
year 6 equates to the year 2004 + 6 = 2010
year 18 equates to the year 2004 + 18 = 2022.

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