A computer program computes a function $\: f \: \{0, 1\}^* \times \{0, 1\}^* \rightarrow \{0, 1\}^*$. Suppose $f(a, b)$ ahs length $\mid b \mid ^2$, where $\mid a \mid$ and $\mid b \mid$ are the lengths of $a$ and $b$. Suppose, using this program, the following computation is performed.
x="01"
for i=1, ... , n do
x=f("01", x)
Suppose at the end, the length of the string $x$ is $t$. Which of the following is TRUE (assume $n \geq 10)?$
- $ t \leq 2n$
- $n < t \leq n^2$
- $n^2 < t \leq n^{\log_2 n}$
- $ n^{\log_2 n} < t \leq 2^{(2n)}$
- $2^{(2n)} < t$