https://file.aiquickdraw.com/mathbot/file/1724751585598xomp332n.jpg

To solve the problem, we need to determine how many bacteria will be in the dirty water pipe after 5 hours, given that the bacteria population doubles every hour.

### Given:
- Initial number of bacteria (\( P_0 \)) = 50
- Doubling time = 1 hour
- Time (\( t \)) = 5 hours

### Formula:
The population of bacteria after \( t \) hours can be found using the formula:
\[
P(t) = P_0 \times 2^t
\]
where:
- \( P(t) \) is the population after time \( t \),
- \( P_0 \) is the initial population,
- \( t \) is the time in hours.

### Calculation:
\[
P(5) = 50 \times 2^5
\]
\[
2^5 = 32
\]
\[
P(5) = 50 \times 32 = 1600
\]

### Answer:
There will be 1,600 bacteria in the dirty water pipe after 5 hours.

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the bacterial population change after 10 hours instead of 5 hours?
2. If the population doubles every 30 minutes instead of every hour, how many bacteria will there be after 5 hours?
3. What would be the population if the initial number of bacteria was 100 instead of 50?
4. How does the growth rate change if the bacteria double every 2 hours instead?
5. What would be the bacteria population after 5 hours if the doubling process was not perfect, with a 90% efficiency?

**Tip:** In exponential growth problems, always check the base and exponent to understand how the population changes over time.

Understand how bacterial population grows exponentially over time with a detailed example calculation. Learn the population growth formula P(t) = P0 * 2^t and apply it to determine the number of bacteria after 5 hours, starting with an initial population of 50.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation