Consider the following three functions. $$f_1 = 10^n \qquad f_2 = n^{\log n} \qquad f_3 = n^{\sqrt{n}}$$ Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

To compare the asymptotic growth rate of the functions, take the natural logarithm (or base-2 logarithm) of each function:

1. For $f_1 = 10^n$:

   $$\log f_1 = \log(10^n) = n \log 10 = \Theta(n)$$

2. For $f_2 = n^{\log n}$:

   $$\log f_2 = \log(n^{\log n}) = (\log n) \cdot (\log n) = (\log n)^2$$

3. For $f_3 = n^{\sqrt{n}}$:

   $$\log f_3 = \log(n^{\sqrt{n}}) = \sqrt{n} \log n$$

Comparing the growth rates of their logarithms for large $n$:

Therefore:

Thus, the increasing order of asymptotic growth rate is $f_2, f_3, f_1$, which corresponds to (D).