exponential growth example would be cell replication or populations. Population is 2 people have 2 kids, those 2 kids have 2 kids, those 2 have 2. In a perfect world it follows 2^n where n is generation. Same with bacterial growth and cell replication.
exponential decay is most commonly taught with atomic half lives and radiation. every time an elements half life expires, half of it is no longer radioactive. so it follows. 1/(2^n) where n is the number of half lives