Is there an explanation to the "exponential" growth of power levels in Z fighters?
One possible answer is that Saiyans get way more powerful than before if they agonize (and survive). It's called Zenkai. This ability is found in pure Saiyan, half-blood and even Cell. 

One example is when Gohan fights Cell, kicks him around, but refuses to kill him. This allows Cell to recover and get way stronger than before, making it very difficult to Gohan to kill him, even with help of other warriors, Vegeta and even dead Goku. In retrospect, Gohan could have single-handedly kill Cell, but he didn't do so at the beginning of their fight.

Not by coincidence, this "ability" make every fight involving Saiyan longer and with plot-twists.

Source: Zenkai - Dragon Ball Wiki