https://file.aiquickdraw.com/mathbot/file/17274315288133cw0p8qu.jpg

The image shows the following mathematical problem:

- **Initial count**: 50,000 (bacteria)
- **Increase percentage**: 2% per hour
- **Formula used** to calculate the amount of bacteria after 2 hours:
  
\[
50000 \times \left(\frac{100 + 2}{100}\right)^2 = 52020
\]

### Explanation:
1. The bacteria count grows at a rate of 2% per hour.
2. To calculate the growth over 2 hours, we apply the percentage increase formula twice (compounding effect).

The factor for 2% growth is \(\frac{100+2}{100} = 1.02\).

After 2 hours, the formula is:
\[
50000 \times 1.02^2 = 50000 \times 1.0404 = 52020
\]

Thus, the number of bacteria after 2 hours is **52,020**.

Would you like more details or have any questions?

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Here are 5 follow-up questions you might find interesting:
1. How would the bacteria count change if the growth rate were 5% instead of 2%?
2. What would happen if the time period were extended to 5 hours?
3. Can this model be extended to non-integer time intervals (e.g., 1.5 hours)?
4. How does compounding affect the total growth over longer periods compared to linear growth?
5. What if there were an initial decrease in the bacteria population?

**Tip**: For continuous growth problems, the exponential growth formula \(P(t) = P_0 e^{rt}\) is often more accurate when applied to real-world situations over small intervals of time.

Initial count = 50,000; Increase percent = 2%; Calculate the amount of bacteria after 2 hours.

Learn how to calculate the growth of bacteria with an initial count of 50,000 and a 2% hourly increase. This problem explores compounding and exponential growth, suitable for high school students in Grades 9-12.

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