From the table provided, it seems that Ahmad and Chris are modeling the growth of bacteria through binary fission, where each bacterium divides into two every minute.

The pattern shows:

• At $t = 0$ minutes, there is 1 bacterial cell.
• At $t = 1$ minute, there are 2 cells.
• At $t = 2$ minutes, there are 4 cells.
• At $t = 3$ minutes, there are 8 cells.
• At $t = 4$ minutes, there are 16 cells.
• At $t = 5$ minutes, there are 32 cells.

This represents exponential growth where the number of cells doubles every minute. The general formula for the number of bacterial cells at time $t$ can be expressed as:

$N(t) = 2^t$

Explanation of the formula:

• $N(t)$: Number of bacterial cells at time $t$.
• $t$: Time in minutes.

Would you like a more detailed explanation of this growth, an exploration of how this connects to real-world bacteria, or assistance with other calculations?

Here are 5 follow-up questions to extend this topic:

1. What would the number of bacterial cells be at $t = 10$ minutes?
2. How would you calculate the time required for the number of cells to reach 1024?
3. If the bacteria's environment supports a maximum of 1000 cells, at what time will the population stop growing?
4. How does binary fission differ from other bacterial reproduction methods?
5. Can we extend this model to include factors like limited resources (logistic growth)?

Tip: In exponential growth, doubling time is constant. To identify the doubling pattern, keep track of when the population doubles and see if it aligns with the formula!