To solve this problem, let's break it down step-by-step:
1. Understanding growth rate: We know that the bacteria double every 20 minutes. This means the population grows exponentially by a factor of 2 every 20 minutes.
2. Total duration: We need to determine the number of bacteria after 120 minutes (which is 2 hours).
3. Number of intervals: To find out how many times the bacteria double in 120 minutes, we divide 120 minutes by the doubling interval, which is 20 minutes.
[tex]\[
\frac{120 \text{ minutes}}{20 \text{ minutes/interval}} = 6 \text{ intervals}
\][/tex]
4. Initial number of bacteria: We start with 1 bacterium.
5. Calculating the final number of bacteria: Since the bacteria double every 20 minutes and we have 6 intervals:
[tex]\[
\text{Final number of bacteria} = 1 \times 2^6
\][/tex]
6. Evaluate the exponentiation:
[tex]\[
2^6 = 64
\][/tex]
Therefore, the correct number of bacteria after 120 minutes is [tex]\( \boxed{64} \)[/tex].
