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The problem presents the exponential function \( P(t) = 100(2)^t \), which models the population of a bacterial colony \( t \) hours after the start of an experiment. We need to interpret the point \((3, 800)\).

### Analysis
1. **Given Function**: \( P(t) = 100(2)^t \)
   - \( P(t) \): Population of the bacteria at time \( t \).
   - \( t \): Time in hours.

2. **Interpretation of the Point \((3, 800)\)**:
   - The point \((3, 800)\) indicates that at \( t = 3 \) (3 hours after the start), the population \( P(3) \) equals 800.

3. **Verification**:
   - Substituting \( t = 3 \):
     \[
     P(3) = 100(2)^3 = 100 \times 8 = 800
     \]
   - This confirms that after 3 hours, the population reaches 800.

### Correct Answer
The correct interpretation is: *After 3 hours, the population of the bacterial colony has increased to 800*. This matches the selected option.

Would you like more details or have any questions about this problem?

### Related Questions:
1. How would the interpretation change if the exponential base were different, such as \( 100(3)^t \)?
2. What does the base \( 2 \) represent in this exponential model?
3. How do you determine the growth rate from an exponential function like \( P(t) = 100(2)^t \)?
4. What would the population be after 5 hours using the same function?
5. How can you determine when the population reaches 1600?

### Tip:
In exponential growth models, the base of the exponent indicates how the quantity changes for each unit increase in \( t \). A base of 2 means the quantity doubles each time \( t \) increases by 1.

The exponential function P(t) = 100(2)^t models the population of a bacterial colony t hours after the start of an experiment. What is the best interpretation of the point (3, 800) in this context?

Learn how to interpret the exponential function P(t) = 100(2)^t that models bacterial population growth, and understand the meaning of the point (3, 800) in this context. This question is suitable for students in Grades 8-10.

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