Question: 2019 Winter Midterm - 11
The function $f : \mathbb{N} \rightarrow \mathbb{N}$ is recursively defined as follows:
$$
\begin{align}
f(0) &= 6, \\
f(n) &= 4 \cdot f(n-1) + 2^{n} \ \ \mathrm{if}\ n \geq 1.
\end{align}
$$
Which of the following is true for all integers $n \geq 0$?
(a)
$f(n) = 7 \cdot 4^{n} - 2^{n}$
(b)
$f(n) = 8 \cdot 4^{n} - 2^{n+1}$
(c)
None of the above.
(d)
$f(n) = 6 \cdot 4^{n} - 2^{n}$