I need help for today on this exercise :

Approximate the data in the following table

with a function of the form

in the sens of least squares for the function

.

I understand the problem and I will simplify it for you, so you can help me. They want me to approximate the data given in the table, via a function of the type

, which is a too complicated problem. Therefore, in order to do it, we take the natural log of

, to approximate a new set of data, which will be

. This is much less complicated to determine a, b and c. After this we just replace a, b and c in f(x) and we're done. But the problem is that I don't know how to get these values.

The problem is simplificated to approximate

with a function of the form

. To get a linear system, I must use the inner product theory to solve the problem.

Let V be the set of

,

,

,

such that f is a function. Let W be a subset of V, so W={...}. Then I define the inner product between x and y as

. From it I must use the normal equations to solve the problem and get a, b and c. But as I don't know how to define W, nor how to construct the normal equations, I'm totally stuck on this.