Answer
$f(x)=2^x, a=5$
Work Step by Step
As $32=2^5$, let $f(x)=2^x$, we have:
$$f'(5)=\lim_{x\to 5}\frac{2^x-2^5}{x-5}=\lim_{x\to 5}\frac{2^x-32}{x-5}$$
Thus we have $f(x)=2^x, a=5$
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