Вы не правильно используете exec, он тут вообще не нужен.
$ man bash
exec [-cl] [-a name] [command [arguments]]
If command is specified, it replaces the shell. No new process
is created. The arguments become the arguments to command. If
the -l option is supplied, the shell places a dash at the begin‐
ning of the zeroth argument passed to command. This is what
login(1) does. The -c option causes command to be executed with
an empty environment. If -a is supplied, the shell passes name
as the zeroth argument to the executed command. If command can‐
not be executed for some reason, a non-interactive shell exits,
unless the execfail shell option is enabled. In that case, it
returns failure. An interactive shell returns failure if the
file cannot be executed. If command is not specified, any redi‐
rections take effect in the current shell, and the return status
is 0. If there is a redirection error, the return status is 1.
