Algebra Level 4

$\begin{array} {r l l } f(0) & =& 2^0 \\ f(1) &=& 2^1 \\ f(2) &=& 2^2 \\ f(3) &=& 2^3 \\ f(4) &=& 2^4 \\ f (5) &=& 2^5 \\ f (6) &=& 2 ^ 6 \end{array}$

If $f(x)$ is a degree 6 polynomial satisfying the above values, then what is the value of $f(13)$?

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