# A bacterial culture starts with 2,000 bacteria and doubles in size every 6 hours. How do you find an exponential model for the size of the culture as a function of time t in hours?

##### 1 Answer

#### Explanation:

One thing we know about bacteria, if there's one, there'll be more.

So that means the rate of growth of the bacteria is dependent on how much of these lil' buggers there is in the start.

In mathematical terms,

Let's rearrange that equation, so we get

Integrate, from

so that means, time is from

Integrating leaves us with

We see that in the next six hours,

So, rearranging the equation after substitution,

Your calculator will help with the finalizing of what

Nevertheless, now you see how the answer comes to as given above.