2022 Cayley Problem 18

At the beginning of the first day, a box contains 1 black ball, 1 gold ball, and no other balls. At the end of each day, for each gold ball in the box, 2 black balls and 1 gold ball are added to the box; this means that at the end of the first day, there are 5 balls in the box. If no balls are removed from the box, how many balls are in the box at the end of the seventh day?

\textbf{(A)}\ 395\quad \textbf{(B)}\ 371\quad \textbf{(C)}\ 389\quad \textbf{(D)}\ 377\quad \textbf{(E)}\ 383

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.