We have exponential growth when the size grows as the function

• $f(t)=ab^t$
for some constants a and b.

Exponential growth arises when the amount added is proportional to the amount we have. For example, early growth of bacteria, where the number of new bacteria is based on how many there are - if you have lots, there are lots to create new ones!

Another example is compound interest, where the interest you earn is proportional to the amount of money you have.

See Carbon Dating.

The formula can also be expressed as $f(t)=ae^{ct}$ where e is Euler's number.

Some well-known sequences grow exponentially, such as the Fibonacci sequence, the Perrin sequence, and solutions to various equations.