I've been given a simple problem: use the quadratic
function to predict the number of
subscribers expected in 2010.
According to the table,
$$\begin{array}{|c|c|}
\hline \text{Year} & \text{Subscribers (millions)} \\ \hline
1985 & 1 \\ \hline
1990 & 11 \\ \hline
2000 & 741\\ \hline
\end{array}$$
I was told to set-up the series of equations like $$A(1985^2) + B(1985) + C = 1$$and so on. However, when I do that and put them in a matrix to solve, I get an answer that is far from correct. Any help in getting me on the right track? I don't know why I'm struggling with this so much… That said, I do suspect I was not told how to set-up this problem correctly.
Best Answer
did you try the system ...
$$A(1985^2) + B(1985) + C = 1 \tag 1 $$
$$A(1990^2) + B(1990) + C = 11 \tag 2 $$
$$A(2000^2) + B(2000) + C = 741 \tag 3 $$
$$ (2)-(1) \implies A(1990^2-1985^2) +5B = 10 \tag 4$$
$$ (3)-(1) \implies A(2000^2-1985^2) +15B = 740 \tag 5$$
now the equation generated from $(5)-3\times (4)$ can be solved for A , sub into (4) and (1) to get B and C