How to approximate table-defined function using non-linear least squares

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I read least squares method and haven`t found a good example of using non-linear least squares.

Problem: I have an arbitrary values for x = 1, 2, 3, 4, 5, therefore, I have a table-defined function. I have to approximate this function using the non-linear least squares method and then extrapolate values for x = 0, 6.

P. S. I attempts to be a programmer, not a mathematician. I appologize and ask you to correct me if something I wrote is wrong.