Say the colony started with 'a' bacteria .
After one hour it had .
After two hours it had .
After three hours it had .
After four hours it will have or the number after three house times 3.
Notice what is changing in this sequence - the exponent. That makes this an exponential (when the variable is in the exponent).
If you want to see this using the formula, then follow this:
Since you can say
Multiply both sides by to get
Plugging this back in to the you get , which is the same as what is in the series above.