Given the model
$\alpha_1 I_k - \alpha_2 I_k^2 = I_{k+1}$ corresponding to measurements shown in the table below
$k$ | 1 | 2 | 3 | 4
$I_k$| 0 | 1 | 10 | 80 |
Determine the least squares estimate of $\alpha_1$ and $\alpha_2$
I got
$A = \begin{bmatrix} I_k&-I_k^2\end{bmatrix} = \begin{bmatrix} 0&0\\1&-1\\10&-100\end{bmatrix}$ and $b = \begin{bmatrix} I_{k+1}\end{bmatrix} = \begin{bmatrix} 1\\10\\80 \end{bmatrix}$
I get $\begin{bmatrix} \alpha_1\\ \alpha_2 \end{bmatrix} = \begin{bmatrix} 10.22\\0.22 \end{bmatrix}$
The graph is
Can someone please tell me if it is correct or not?
