UPDATE 2017: This whole post is of historical interest only. We have gotten rid of exponential roads in Beeminder!
Once in a while someone tries to set up a yellow brick road where the steepness automatically increases by, say, 10% each week. It seems like a so-called exponential road (available with custom goals, which is one of the Bee Lite premium perks) might be just the ticket.
But exponential roads can’t be used that way. They can be used for weight loss, for example, when you want the daily or weekly decrease to be a function of your current weight  (we recommend a max loss rate of 1% of your weight per week). But we don’t have a way to make the rate depend on what the previous rate was. I think the confusion here stems from the fact that Beeminder is plotting the cumulative total on the y-axis. Having the rate depend on that cumulative total doesn’t make sense.
“That’s not as onerous as it sounds and you’ll want to reassess the steepness of your road weekly anyway.”
What we recommend is that you just manually nudge the rate every week with the road dial. We think you’ll find that’s not as onerous as it sounds and that you’ll want to reassess the steepness of your road weekly anyway. Again, you don’t actually want exponential goals unless the rate depends on the current value being plotted on the y-axis. Which doesn’t make sense when the cumulative total is what’s being plotted.
Something like “losing 0.3% of your bodyweight per week” (much more realistic than the ultra hardcore 1%/week, btw) is where it does make sense. Or like our meta graphs where we want to grow at some percentage per week.
The point is, if you’re excited about tweaking the heck out of your yellow brick roads then, first of all, we’re always excited to hear about what crazy things you’re beeminding, and you may find our Bee Lite plan worth it for the added customization, but it turns out most people whose eyes light up at the idea of an exponential road have the wrong idea. Of course you can always hack something like that up with our API. 
 Technically it’s a function of where your road is, but if you’re using the yellow brick road as a guide (like most folks), then that’s roughly the same thing. If you’re way ahead of schedule, it won’t be the same thing, but through the beauty of exponential curves, it soon will be!
 One of our most intrepid users (but anonymous and unlinkable, sorry) has written herself a script that adjusts the road slope nightly, based on her actual progress on the goal. It’s not exponential (though you can pick the algorithm) but it does keep her slopes increasing automagically over time. (Watch out for holidays, deliberate slowdowns, and archived goals, if you automate something like this!) We’ll hopefully convince her to share it at some point because that and the other stuff she’s hacked up — we’ve had glimpses on Akratics Anonymous — is pretty epic. UPDATE: We got the all-clear to identify Essy by her pseudonym and point to the post on Akratics Anonymous where she shared her PHP code.
Image credit: Connie Szabo Schmucker while riding the Hilly Hundred bike tour in Indiana. If you’re in that part of the country we recommend it. It’s beautiful and very hilly!