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Math·Advanced Math·Nonlinear functions

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$$f(x)=29(b{)}^x+c$$The function $f$ is defined by the given equation, where $b$ and $c$ are constants and $b>1$. In the xy-plane, the graph of $y=f(x)$ contains the point $(0,44)$. For all values of $x$, $f(x)>k$, where $k$ is a constant. What is the greatest possible value of $k$?

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