Perl 5, 36 31 bytes
printf"%.2f",1.0644944**($_-31)
Command line one-liner examples:
echo 52 | perl -ne 'printf"%.2f\n",2.71828**(($_-31)/16)'
echo 52 | perl -ne 'printf"%.2f\n",1.06449445**($_-31)'
echo 52 | perl -ne 'printf"%.2f\n",1.06449445**($_-31)'
echo 52 | perl -ne 'printf"%.2f",1.06449445**($_-31)'
echo 52 | perl -ne 'printf"%.2f",1.0644944**($_-31)'
for a in {1..122};do echo "Man: $a Dog: "`echo $a|perl -ne'printf"%.2f\n",1.0644944**($_-31)'`;done