Docker Ubuntu PATH won't save

I am using a Ubuntu image (Ubuntu 20.04). Essentially, I am trying to modify my PATH permanently so that every time I start the container I don't have to manually edit the PATH to find the new items I have installed. However, no matter what I do I am unable to make the change permanent. I have sunk some considerable time into the image, so I would very much like to find a solution so I don't have to rebuild the whole thing.

Here is the shell information

#ps -p $$
  PID TTY          TIME CMD
    9 pts/1    00:00:00 sh 

# echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin

# PATH=$PATH:/kraken
# echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/kraken

#. ~/.profile

Now when I restart the container:

#echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin

Basically, the PATH was not saved. I have been through so many blogs and stack and I can't find anything that sticks. Any help would be really appreciated.

Copyright Notice：Content Author:「DJFast」，Reproduced under the CC 4.0 BY-SA copyright license with a link to the original source and this disclaimer.
Link to original article：https://stackoverflow.com/questions/65673632/docker-ubuntu-path-wont-save