Question

Bacteria can divide in every 20 minutes. So, 1 bacterium can multiply to 2 in 20 minutes, 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents, then evaluate.

Answer 1

To find the number of bacteria after 6 hours with a division time of 20 minutes, one calculates the number of divisions (18) and uses the formula 2^18, resulting in 262,144 bacteria.

Step-by-step explanation:

The question involves calculating the number of bacteria after a given period of time, specifically 6 hours, assuming the bacteria divide every 20 minutes. This is a classic example of exponential growth.

First, we need to determine the number of intervals (or generations) that occur within the 6 hours, which we can do by dividing the total time by the duration of one division cycle. Since there are 60 minutes in an hour, 6 hours is equivalent to 360 minutes. Dividing 360 minutes by 20 minutes per cycle gives us 18 cycles.

The number of bacteria will double with each cycle, which can be represented by the exponential formula 2^n, where n is the number of cycles. Therefore, after 18 cycles, the number of bacteria will be 2^18.

Now, we need to calculate the actual number of bacteria. 2^18 can be simplified to 262,144. So, after 6 hours, there would be 262,144 bacteria.