there is 100 bacteria in a petri dish. every 30 minutes the bacteria doubles. how muchbacteria will there be in 3 hours.
100 >> 200
200 >> 400 >> 1 hour
400 >> 800
800 >> 1600 >> 2 hours
1600 >> 3200
3200 >> 6400 >> 3 hours
To find out how much bacteria will be there in 3 hours, we need to calculate the number of times the bacteria doubles in that time period.
Since the bacteria double every 30 minutes, we can calculate how many times they will double in 3 hours (180 minutes) by dividing 180 by 30.
180 minutes / 30 minutes = 6
So, the bacteria will double 6 times in 3 hours.
Now let's calculate the total number of bacteria after 6 doublings:
Starting with 100 bacteria, they will double once to become 200, then double again to become 400, and so on until the sixth doubling.
Starting with 100 bacteria and doubling 6 times, we can use the formula:
final amount = starting amount × (doubling factor)^number of doublings
In this case, the doubling factor is 2 and the number of doublings is 6.
final amount = 100 × (2)^6
final amount = 100 × 64
final amount = 6400
Therefore, there will be 6400 bacteria in the petri dish after 3 hours.