Exponential functions can have any base, not just e. In this case, the colony of bacteria is trippling every hour. So the base is 3.

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:

or

Since you can say

Multiply both sides by to get

Then .

Plugging this back in to the you get , which is the same as what is in the series above.