Agreed, it increases linearly. But now think about the cost of change without tests. The longer you wait to introduce the change the more you will have to change (increases exponentially). If this code was fully tested and maybe refactored (isolated) when the need arises, the cost of change would almost go to 0 because you would only have to implement a new feature without touching the old code.
Everything has a cost. TDD (and Refactoring) increases the cost of implementation (linearly), but they greatly reduce the cost of change. Without TDD (and refactoring) the cost of change might become exponential and impossible to catch up to.