Calculating Powers Problem: a researcher is studying bacteria growth, and she finds that every hour, the number of bacteria doubles. If she starts with 3 bacteria, what will the number of bacteria  be after 5 hours? Write your answer in terms of powers of 2

To calculate the number of bacteria after 5 hours, we can apply exponential growth.

Given:
- The number of bacteria doubles every hour.
- The initial number of bacteria is 3.
- The duration is 5 hours.

The formula for this type of growth is:

\[
\text{Number of bacteria} = \text{initial number} \times 2^n
\]

Where:
- \(\text{initial number} = 3\)
- \(n = 5\) (the number of hours).

Thus, after 5 hours, the number of bacteria will be:

\[
\text{Number of bacteria} = 3 \times 2^5 = 3 \times 32
\]

So, the number of bacteria in terms of powers of 2 is:

\[
3 \times 2^5
\]

This represents the number of bacteria after 5 hours.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the number of bacteria after 10 hours?
2. How would the formula change if the bacteria tripled every hour?
3. If the researcher starts with 10 bacteria, what will the number be after 3 hours?
4. How would you solve this if the bacteria only increased by 50% each hour instead of doubling?
5. What is the general formula for exponential growth in bacteria populations?

**Tip:** Exponential growth occurs in many real-world scenarios, such as population growth, compound interest, and radioactive decay.

Calculating Powers Problem: a researcher is studying bacteria growth, and she finds that every hour, the number of bacteria doubles. If she starts with 3 bacteria, what will the number of bacteria be after 5 hours? Write your answer in terms of powers of 2.

Discover how to calculate bacteria growth using powers of 2. Starting with 3 bacteria and doubling every hour, find out how many bacteria there will be after 5 hours. This problem is ideal for understanding exponential growth concepts in Grades 6-8.

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