Some species of bacteria can copy their DNA and divide every 40 minutes. If a colony of 100 of these such bacteria begins with a population of 12 at noon, how many will they be by 6pm?

Bacteria are single-celled organisms. When they copy their DNA and divide, the population will double.

Let's start off by finding how many times the population will divide.

Our replication period is 6 hours - from noon until 6pm. We know that this species of bacteria divides every 40 minutes.

We will start off by finding our total number of minutes.

There are 60 minutes in each hour. We have a 6 hour period.

6*60 = 360 minutes

Next, we will divide our total number of minutes by 40 minutes.

360/40 = 9

We now know that our bacteria will divide 9 times.

Now, let's figure out how many bacteria we will have by 6 pm.

Every 40 minutes, the colony will double in size. This will happen 9 times.

We will start off with a colony of 100. Let the bolded numbers 0-9 represent how many times the bacteria have divided.

0: 100 - the starting size of the population

1: 200 - the population doubles for the first time

2: 400 - the population doubles a second time

3: 800 - the population doubles the third time

4: 1600 - the population doubles for the fourth time

5: 3200 - the population doubles a fifth time

6: 6400 - the population doubles the sixth time

7: 12800 - the population doubles for the seventh time

8: 25600 - the population doubles the eighth time

9: 51200 - the population doubles the ninth time

After 6 hours, the population will double 9 times. We have determined that the population at that time will be 51200 bacteria.