Question

A bacterium is in a glass. Every second it splits in half. Each of the resulting bacteria splits in half the following second, and so on. The glass is filled a minute later. In what time was the glass half-full?

a) 59 seconds
b) 30 seconds
c) 58 seconds
d) 1 second

Answer 1

The glass is half-full at 59 seconds.

Step-by-step explanation:

To answer this question, we need to understand the concept of exponential growth. In this scenario, the bacteria in the glass double every second. So, after 1 second, there are 2 bacteria; after 2 seconds, there are 4 bacteria; after 3 seconds, there are 8 bacteria, and so on.

In total, there are 60 seconds in a minute. Since the glass is filled a minute later, we need to determine the time at which it is half-full. At 59 seconds, there are still only 2^59 bacteria in the glass, which is less than half of the final population.

Therefore, the correct answer is a) 59 seconds.