One bacterium divides into two bacteria every 3 minutes.If two bacteria multiply enough to completely fill a petri dish in 3 hours, how long will it take one bacterium to fill the dish?
A)3 hours
B)3 hours 9 minutes
C)3 hours 4 minutes
D)3 hours 3 minutes
E)3 hours 6 minutes

Question

Quizplus · Accepted Answer

If one bacterium divides into two every 3 minutes, the number of bacteria in the dish will double every 3 minutes. 
In 3 hours, or 180 minutes, there are 60 minutes in an hour * 3 hours = 180 minutes. 
Since the bacteria need to completely fill the dish, we can set up the equation: 
2^n = total number of bacteria needed to fill the dish 
2^n = 2*2*2*2 ... (n times)
We don't know n yet, but we do know that it takes 180 minutes to get to this number of bacteria. 
Let's see how many times bacteria double in 180 minutes: 
180 / 3 = 60 doublings 
So n = 60. 
Plugging that in to our equation: 
2^60 = total number of bacteria needed to fill the dish 
Now we need to find out how long it takes for one bacterium to become 2^60 bacteria. To do that, we need to reverse the process: 
2^0 = 1 
2^1 = 2 
2^2 = 4 
and so on. 
The number of doublings needed to get to 2^60 is simply 60, so it would take 60 * 3 minutes = 180 minutes = 3 hours.

One Bacterium Divides into Two Bacteria Every 3 Minutes