At 8Am population of bacteria is 100,at 10Am population of bacteria is 200,At 12PM population of bacteria is 400,At 2PM population of bacteria is 800.If the pattern continues what will the bacteria population be at 6.00 pm

3200 bacteria will be living.

Please give me detail step

They double in number every 2 hours

8:00 -- 100
10:00 -- 200
12:00 -- 400
2:00pm -- 800
4:00 pm -- 1600
6:00pm -- 3200

To determine the pattern and predict the bacteria population at 6:00 PM, we can analyze the growth rate. From the given data, we notice that the population doubles every 2 hours.

Starting with the initial population of 100 bacteria at 8:00 AM, we can observe the increments as follows:
8:00 AM - 100
10:00 AM - 200 (doubled from 8:00 AM)
12:00 PM - 400 (doubled from 10:00 AM)
2:00 PM - 800 (doubled from 12:00 PM)

Based on this pattern, we can see that the population doubles every 2 hours. To find the population at 6:00 PM, we need to determine how many doubling cycles occur between 2:00 PM and 6:00 PM.

Since there are 4 hours between 2:00 PM and 6:00 PM, there are two 2-hour doubling cycles in that time period. Therefore, we can calculate the population at 6:00 PM as follows:

2:00 PM - 800
4:00 PM - 1,600 (doubled from 2:00 PM)
6:00 PM - 3,200 (doubled from 4:00 PM)

So, based on the given pattern, the bacteria population at 6:00 PM would be 3,200.