To determine which statement is true, let's analyze the growth of the bacteria in samples A and B over time.

Given:

• Initial population in both samples A and B: 1,000 bacteria.
• Growth rate for sample A: 10% per week.
• Growth rate for sample B: 150 bacteria added per week.

Let's calculate the population for each sample week by week to verify the statements.

1. Sample A (Exponential Growth): Each week, the population in sample A is multiplied by 1.10 (a 10% increase).

   • Formula: $\text{Population}_A = 1000 \times (1.10)^n$, where $n$ is the number of weeks.

2. Sample B (Linear Growth): Each week, 150 bacteria are added to the population in sample B.

   • Formula: $\text{Population}_B = 1000 + 150 \times n$, where $n$ is the number of weeks.

Now, let's calculate for each relevant week to check each statement:

Week-by-Week Calculations

Week 6:

• Sample A: $1000 \times (1.10)^6 \approx 1771$
• Sample B: $1000 + 150 \times 6 = 1900$

Week 7:

• Sample A: $1000 \times (1.10)^7 \approx 1948$
• Sample B: $1000 + 150 \times 7 = 2050$

Week 8:

• Sample A: $1000 \times (1.10)^8 \approx 2143$
• Sample B: $1000 + 150 \times 8 = 2200$

Week 9:

• Sample A: $1000 \times (1.10)^9 \approx 2358$
• Sample B: $1000 + 150 \times 9 = 2350$

Analysis of Statements

1. In week 6, the number of bacteria in sample A is more than that in sample B.

   • False: Sample A has 1771 bacteria, and Sample B has 1900 in week 6. Sample B has more bacteria.

2. The number of bacteria in sample A exceeded that in sample B for the first time in week 9.

   • True: In week 9, Sample A has 2358 bacteria, and Sample B has 2350. This is the first time Sample A exceeds Sample B.

3. The number of bacteria in sample B exceeded that in sample A for the first time in week 8.

   • False: Sample B has been greater than Sample A from the start up until week 8.

4. The number of bacteria in sample A is 1,771 in week 7.

   • False: The population in Sample A is approximately 1,771 in week 6, not week 7.

Conclusion

The correct answer is:

• The number of bacteria in sample A exceeded that in sample B for the first time in week 9.

Would you like further details on any of these calculations?

Here are 5 related questions for practice:

1. What would be the population of each sample at week 10?
2. How many weeks would it take for Sample A to double its initial population?
3. At what week will Sample A's population be approximately 3000?
4. What is the difference in population between the two samples at week 12?
5. How would the calculations change if Sample B's weekly increase was instead a 20% growth?

Tip: For exponential growth calculations, understanding the compound growth formula is essential for accuracy.