Tasnim A. answered • 30d

Undergraduate Computer Science Student

Hello!

Let's start by breaking this question down.

If **bacteria reproduce**, then **each bacterium adds one bacteria to the total count of bacteria**. Put simply, **the total number of bacteria is doubled**.

We are also the **rate at which it doubles**, as well as the **total time elapsed since the count of 200**.

The bacteria doubles **every 20 minutes**. We are given a time frame of **2 hours**. We need to relate these measurements of time somehow– **how many 20 minute intervals are in 2 hours?**

Well, there are **120 minutes** in 2 hours, and **120 ÷ 20 = 6**.

Therefore, we know that the **bacteria will double 6 times**.

Now that we know this, we can calculate our answer!

The obvious approach is to simply multiply 200 by 2, then that product by 2, and so on until it's been done 6 times. While that method will give you the correct answer, there is a faster way to get to the answer!

We know that we will **multiply our total bacteria count by 2, 6 times**. In other words, **200 * 2 * 2 * 2 * 2 * 2 * 2**. In other words, **200 * 2**^{6}. In other words, **200 * 64**.

Therefore, we can simply **multiply 200 by 64.**

Our final answer is: ** 12,800** .

I hope this response was helpful! If you have further questions or need more clarification, please feel free to message me!