I'm having trouble to understand the consign of the exercise. It says "Approximate the data of the following table with a model of the form f(x)~ ae^{bx} in the meaning of least squares for the function ln(f(x)).
\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline y & 8.1 & 3 & 1.1 & 0.5\end{array}"
My approach : I believe they ask me to approximate the data in the table, with a function of the form f(x)=ae^{bx}, so I wonder what the ln(f(x)) is about. So I didn't considered it. I made the least squares, that is f(a,b)=\sum_{i=-1}^2 (ae^{bx}-y_i)^2. I did the partial derivative with respect to a and equaling it to 0 I got the following equation : ae^{bx}-c=0, where c is \sum_{i=-1}^2 y_i.
I did the same with the partial derivative with respect to b, except that I had to suppose a and b different from 0 to make some division. And I got exactly the same equation as I got for the first partial derivative. Therefore the system has no solution, which is not normal considering the problem given. It means I made an error, or I misinterpreted the problem. Can you help me?