CAYLEY 2022 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?

Answer Choices
A. 395
B. 371
C. 389
D. 377
E. 383