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Math·Advanced Math·Nonlinear functions

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The function $f$ is defined by the equation $f(x)=9^x+b$, where $b$ is a constant. In the $xy$-plane, the graph of $y=f(x)$ contains the points $(0,27)$ and $(3,p+16)$, where $p$ is a constant. What is the value of $p$?

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