L = {$(n,w)$ $w$ is a binary representation of the n-th fibbonacci number} membership decision problem

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I am a student currently studying Computational Models. I still don't have a full understanding of the subject and was wondering about languages of the form $L = \left \{(n,w) | f(n) = w \right \}$ which we didn't discuss in class.

For starters, consider the language:

L = {$(n,w)$ $|w$ is a binary representation of the n-th Fibonacci number}

And the decision problem: "is $(n,w) \in L$?"

Is this problem a member of $P$ - The class of decision problems which has a deterministic Turing machine that decides it in poynomial time?

I suspect this is correct since it has a closed formula, but am not sure of the capabilities of Turing machines in calculating this kind of functions.

Thanks