Question

Under ideal conditions, some common bacteria can divide and double their numbers in less than 1/2 hour. Suppose one spring day at 6 AM, a few bacteria fall into a can of strawberry syrup in a broken garbage bag behind a snack bar. The population doubles every 20 minutes. But by 6 PM the bacteria are overcrowded and dry and their food is gone. At one point during the day, some forward – thinking bacteria get the idea that they are facing a crisis. Their numbers are growing exponentially and they are using up their space and food at an ever – increasing rate. At what time do you think that idea would come? Explain.

Answer 1

Considering exponential growth, if bacteria double every 20 minutes and the environment becomes fully exhausted by 6 PM, the 'forward-thinking bacteria' would realize they are facing a crisis at 5:40 PM, when the jar is half full.

Similarly, in a 24-hour growth scenario with doubling every 10 minutes, the jar would be half full at 11:50 PM.

Step-by-step explanation:

Exponential growth is when a population doubles at a regular interval. In the example given, the bacteria in the strawberry syrup double in number every 20 minutes.

Because the doubling is constant, the jar would be half full exactly one doubling period before it is completely full. If we agree that 'overcrowded and dry and their food is gone' means the jar is just full at 6 PM, then backtracking one doubling period (20 minutes) means the jar would be half full at 5:40 PM.

This realization of resource limitation should ideally strike the bacteria at this point where the space is still ample. A similar situation is presented where the bacteria double every 10 minutes, and the jar becomes full in exactly 24 hours, starting at midnight. Here, the jar would be half full at 11:50 PM the previous night.

Recognizing the pattern of exponential growth, we can see that the important concept is not how full the jar is at a given moment, but rather, how quickly it is filling up.