PHP exponential growth by certain factor in given steps

PHP exponential growth by certain factor in given steps

I can't figure out how to do this in PHP.
What I have is:
$loops=10; $factor=5; $start=20; $end=80;
So I want to start the loop at 20 and reach the exact number 80 by doing
10 loops and the difference between the output-number per loop should
somehow be influenced by the factor 5 or whatever number. So all together
these numbers would be an exponential curve.
Thanks