Answer:
2,048 cm
Explanation:
There are 4 weeks in a month, and the fish doubles in length every week 
Let's put this into a table: (attached picture)
First we start off at 0.5 cm in week 0 (this is week 0 because you just bought the fish). 
Then, the length doubles in week 1, so the fish becomes 1 cm. 
In week 2, the fish's length doubles again to become 2 cm. 
In week 3, the length doubles to become 4 cm. 
So on, and so on until we reach a length of 2048 cm. 
Therefore, after 3 months the fish's length will be 2,048 cm. 
I hope this helps! Good luck, and if you have any questions please let me know in the comments!