What about adding "echo sleep 0.01 >> ~/.bashrc" to their .bashrc (or whichever shell config file is used)?
EDIT: I misunderstood it as executing
echo sleep 0.01 >> ~/.bashrc
once instead of adding that line to .bashrc – even though that's exactly what you wrote...The first time it does it once, the second time the statement is there twice so it does it twice, then 4, 8, 16, etc. ?
echo sleep 0.01 >> ~/.bashrc
adds this to .bashrc; sleep 0.01
It doesn't add itself, so the sleep tie grows linear by 0.01sec each time a shell is opened.