Propositional Logic Time complexity
Your question hints at multiple misconceptions which I'm going to address.


  If i have a propositional logic formula, every time i add a variable the number of interpretation grow up by 2.


First, let's be clear about terminology.


variable vs literal -- the formula $a \lor b \land a$ has three literals but two variables.
model vs interpretation -- every logical formula has exactly one of two possible interpretations, true and false. 


It would be correct to say: the number of models grows exponentially (with base 2) in the number of variables.


  So, is the time complexity of the SAT problem of propositional logic a $O(2^x)$?


No, that does not follow.


What is $x$? In complexity theory, we usually express complexity in the input length. So if $x$ is the number of literals, that thought makes sense; if it's the number of variables, it does not. However, in the worst cases (if we consider search space alone), the number of variables and literals is the same.
The number of possible models (e.g. valuations of the variables) alone is not trivially an upper bound on the complexity. The brute-force algorithm also has to evaluate the formula for every candidate, so you have to add a linear factor at least (depends on the computational model and cost model you use).
When somebody says, "the complexity is X" that implies a lower bound in addition to an upper bound. Your observation does not provide a lower bound, even after correction.

That is because the size of the search space does not correlate with solving complexity. Take sorting, for instance: finding the correct permutation has a search space of size $n!$ and yet we can solve the problem in linearithmic time. SSSPP is another common example.