https://file.aiquickdraw.com/mathbot/file/1727186267022u3ktomxo.jpg

The problem in the image reads:

- An Amoeba splits into two every 20 minutes. If initially there are 50 Amoeba, how many Amoebas will there be after 2 hours?

Let's break this down:

1. Every 20 minutes, the amoeba population doubles.
2. In 2 hours, there are \( \frac{120}{20} = 6 \) doubling periods (since 2 hours = 120 minutes, and each doubling happens every 20 minutes).

The formula for exponential growth in this context is:
\[
N(t) = N_0 \times 2^n
\]
where:
- \(N(t)\) is the population after time \(t\),
- \(N_0 = 50\) is the initial population,
- \(n = 6\) is the number of doubling periods.

Now calculate the final population:

\[
N(2 \, \text{hours}) = 50 \times 2^6 = 50 \times 64 = 3200
\]

Thus, after 2 hours, the amoeba population is **3,200**.

The correct answer is **c. 3,200**.

Would you like further details or have any questions? 

Here are 5 related questions for further exploration:
1. What would the amoeba population be after 3 hours, given the same conditions?
2. How does the amoeba population grow if the doubling time changes to 30 minutes instead of 20 minutes?
3. What happens if the initial number of amoebas is 100 instead of 50?
4. Can you generalize a formula for any initial population and doubling time?
5. What if some amoebas die off every hour — how would that affect the calculations?

**Tip:** Exponential growth problems are common in biology and finance; understanding the doubling time is crucial for such models!

An Amoeba splits into two every 20 minutes. If initially there are 50 Amoeba, how many Amoebas will there be after 2 hours?

Learn how to calculate amoeba population growth using exponential doubling. Starting with 50 amoeba, find out how many exist after 2 hours when they double every 20 minutes. Suitable for students in Grades 8-10.

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