PS1 is reset after using exec (bug or feature?)

[Kai Lindenberg]

Configuration Information [Automatically generated, do not change]:
Machine: i686
OS: linux-gnu
Compiler: gcc
Compilation CFLAGS:  -DPROGRAM='bash' -DCONF_HOSTTYPE='i686' 
-DCONF_OSTYPE='linux-gnu' -DCONF_MACHTYPE='i686-pc-linux-gnu' 
-DCONF_VENDOR='pc' -DSHELL -DHAVE_CONFIG_H  -I.  -I. -I./include 
-I./lib  -mcpu=pentium3 -march=pentium3 -O3 -pipe
uname output: Linux schleppi 2.4.21-acpi-20030619 #5 Sat Oct 11 
18:13:05 CEST 2003 i686 Pentium III (Coppermine) GenuineIntel 
GNU/Linux
Machine Type: i686-pc-linux-gnu

Bash Version: 2.05b
Patch Level: 0
Release Status: release

Description:
        I don't know if this a feature, but then please tell me why 
        PS1 gets reset when I exec another bash script.

Repeat-By:
        bash-2.05b$ cat<<___END>killmyps1
        > #!/bin/bash
        > /bin/bash
        > ___END
        bash-2.05b$ chmod 755 killmyps1
        bash-2.05b$ export PS1="My Funny Prompt: "
        My Funny Prompt: exec ./killmyps1
        bash-2.05b$


Greetings from Wersau.

Kai