Continuous Everywhere but Differentiable Nowhere

So I posed the more generalized question to  Monday Math Madness 6, which read: 
Start with 500 gallons of mayonaise.
1) Mix in 3 gallons of mayonaise and 7 gallons of ketchup. Stir until completely mixed.
2) Remove 10 gallons of the mixture.
3) Repeat steps 1 and 2 until the mixture is approximately 40% mayonaise and 60% ketchup (200 [...]

Here is my proposed solution to MMM6. (Questions, for the uninitiated or forgetful, are here.)
I actually found these problems to be on the easier side (solved both parts in less than 30 minutes), but I tend to be hasty when I work things out, and overconfident in my thinking, so chances are I’m not right [...]