The image discusses bacterial growth through binary fission, where bacteria divide every 20 minutes under optimal conditions. Here's the breakdown:

• Initial Information: Bacteria reproduce by splitting into two every 20 minutes.
• Question: If the initial number of bacteria is $a$, how can the total number of bacteria after 2 hours be expressed?

Step-by-step solution:

• Time Interval: 2 hours = 120 minutes.

• Number of Divisions: Since bacteria divide every 20 minutes, the number of divisions in 2 hours is: $\frac{120 \, \text{minutes}}{20 \, \text{minutes/division}} = 6 \, \text{divisions}.$

• Bacterial Growth Formula: After $n$ divisions, the total number of bacteria can be represented as: $\text{Final amount} = a \times 2^n.$ Where $a$ is the initial number of bacteria and $n$ is the number of divisions.

• After 6 divisions, the total number of bacteria is: $a \times 2^6.$

• The correct expression is: $\boxed{a \times 2^6}.$ This corresponds to option c from the provided multiple-choice answers.

Would you like more details or have any questions? Here are five related questions to expand the discussion:

1. How would the number of bacteria change if the division time were reduced to 15 minutes?
2. How can we calculate the total number of bacteria after 3 hours instead of 2 hours?
3. What mathematical model best describes exponential bacterial growth?
4. How does temperature influence bacterial reproduction rates?
5. What is the biological significance of exponential bacterial growth in real-world scenarios?

Tip: In bacterial growth, exponential functions are key to modeling how populations expand over time under optimal conditions.