The definition of the derivative, applied to $f(x) = 4^x$, results in the formula $f'(x) = k \cdot 4^x$ where $$k = \lim_{h \rightarrow 0} \frac{4^h - 1}{h} .$$

The value of the constant $k$ cannot be determined using the usual tricks for evaluating limits. Using your calculator, approximate the constant $k$, rounded to three significant figures. $\vphantom{A^A}k \approx$ .