We maintain a web application for a client who demands that new features be added at a breakneck pace. We've done our best to keep up with their demands, and as a result the code base has grown exponentially. There are now so many modules, subsystems, controllers, class libraries, unit tests, APIs, etc. that it's starting to take more time to work through all of the complexity each time we add a new feature. We've also had to pull additional people in on the project to take over things like QA and staging, so the lead developers can focus on developing.

Unfortunately, the client is becoming angry that the cost for each new feature is going up. They seem to expect that we can add new features ad infinitum and the cost of each feature will remain linear.

I have repeatedly tried to explain to them that it doesn't work that way - that the code base expands in a fractal manner as all these features are added. I've explained that the best way to keep the cost down is to be judicious about which new features are really needed. But, they either don't understand, or they think I'm bullshitting them. They just sort of roll their eyes and get angry. They're all completely non-technical, and have no idea what does into writing software.

Is there a way that I can explain this using business language, that might help them understand better? Are there any visualizations out there, that illustrate the growth of a code base over time? Any other suggestions on dealing with this client?