Question

The number of users y (in millions) for a certain website between November 2008 and January 2009 can be modeled by the equation \(\ y=ax^2+bx+c \), where x represents the age of the user. Using the ordered pair (15,1), (25,8), and (35,3), create a system of linear equations in three variables for a, b, and c. Do this by substituting each ordered pair into the model, creating an equation in three variables. Solve the resulting system to find the coefficients of the model. Then use the model to predict the number of new users for the website who were 20 years old.

Answer 1

In your model equation, you have 3 unknowns (a,b and c). But you have 3 pairs (x, y), then you substitute these pairs in the model and get 3 linear equations. Solve them for a,b and c. now you have your model: y = ax^2 + bx + c, now just substitute the value x=20 and find y

Answer 2

It was
\(\Huge y=\frac{-3}{50}x^2+\frac{31}{10}x-32\)
And for the second part it was

\(\Huge 6~million\)

Answer 3

I don't even know how you get that ^^

Answer 4

using the pairs (15,1), (25,8) and (35,3), we get:
First pair:
1 = a*15^2 + b*15 + c
Second pair:
8 = a*25^2 + b*25 + c
Third pair:
3 = a*35^2 + b*35 + c

Now you have this linear system of equations:
a*15^2 + b*15 + c = 1
a*25^2 + b*25 + c = 8
a*35^2 + b*35 + c = 3

Sorlve for a, b and c

Answer 5

Oh
225a+15b+c=1
625a+25b+c=8
1225a+35b+c=3

a=-.06
b=3.1
c=-32
Thanks you so much...

Answer 6

And then I make the equation and plug in 20.. I got it.

Answer 7

\(\Huge\cal\color{blue}{Thank~you~so~much!!}\)

Answer 8

That's it!

Answer 9

No problem ;)