Compounding and exponential growth are different ways to express similar ideas: things can grow quickly!
If you look on graphs of exponential growth they are frequently described as "hockey sticks." They are fairly flat and then shoot up at the end.
1. If algae is doubling every day and completely fills a lake in 30 days on which day will the lake be half full?
It will be half full on the 29th day!
2. Investing in yourself will compound your abilities
Thanks to @randomroger for this one! Very true. The more you do, the more you can do.
3. Minimum payments: If you pay less than your interest you will never get out of debt!
4. Saving in a 401k: $4000 per year with employer match becomes $756,000 after 35 years! That is $140,000 pre-tax dollars going in.
5. Cats: one pair of cats can theoretically generate 634 cats after 4 years and after 10 years there can be over 3.5 million cats!
6. Nuclear explosions
Infections can grow exponentially, as the world found out:
8. Combining technologies 1+1=3
This is more about compounding than exponents. For example, when you take advancement in materials, batteries, miniaturization, computer networks and processing speed you get "smart phones." I wonder how much longer we will call these devices "phones!"
9. Moore's Law:
The number of transistors in an integrated circuit has been doubling every 18 months since 1965.
10. Compound Bow
These machines have a system of cams to manage the bow tension. They can launch arrows at astonishing speeds and have reduced holding weights. It is much easier to hold these bows still than a traditional bow: