How does counting mutually exclusive license-plate lengths illustrate addition and exponential growth?

"Every car in the state of Virginia must be issued its own license plate number. This one requires a bit more thought, since not all license numbers have the same number of characters. In addition to “SED4756” and “PXY1927” you can also have “DAWG” or “LUVME” or even “U2”. The trick is to divide up our set into mutually exclusive subsets, and then add up the cardinalities of the subsets. If only 7 characters fit on a license plate, then clearly every license plate number has either 1, 2, 3, 4, 5, 6, or 7 characters. And no license plate has two of these, so they’re mutually exclusive subsets, and safe to add. Be careful not to cavalierly add the cardinalities of non-mutually-exclusive sets! You’ll end up double-counting items. If every character must be either a letter or a digit, then we have 26 + 10 = 36 choices for each character. The total number of plates is therefore: 36⁷ + 36⁶ + 36⁵ + 36⁴ + 36³ + 36² + 36 = 80,603,140,212 plates. If Virginia decided that all license plates had to have the full 7 characters, the new total number of plates would turn out to be 36⁷ = 78,364,164,096 plates. We’ve hardly lost anything by scrapping all the less-than-7-character plates. This is a powerful illustration of exponential growth: when you modify the exponent, going from something like 36⁶ to 36⁷, you get astronomically larger very, very quickly."