Question 554457
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.
{{{graph(600,600,-5,35,-20,200,.485x^2-1.694x+.315,150)}}}
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.