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The initial number of bacteria in a culture is 12,000. The culture doubles each day. Determine how many bacteria are present after 6 days.

A. 72,000 bacteria
B. 768,000 bacteria
C. 76,800 bacteria
D. 384,000 bacteria

Sagot :

GinnyAnswer
To determine how many bacteria are present after 6 days, we need to understand the concept of exponential growth. In this scenario, the number of bacteria doubles every day.

Here's the step-by-step solution:

1. Identify the initial number of bacteria:
- The initial number of bacteria is 12,000.

2. Understand the doubling process:
- Each day, the number of bacteria doubles. This means we multiply the current number of bacteria by 2 every day.

3. Calculate the number of bacteria each day:
- Day 0 (initial day): 12,000 bacteria
- Day 1: [tex]\( 12,000 \times 2 = 24,000 \)[/tex] bacteria
- Day 2: [tex]\( 24,000 \times 2 = 48,000 \)[/tex] bacteria
- Day 3: [tex]\( 48,000 \times 2 = 96,000 \)[/tex] bacteria
- Day 4: [tex]\( 96,000 \times 2 = 192,000 \)[/tex] bacteria
- Day 5: [tex]\( 192,000 \times 2 = 384,000 \)[/tex] bacteria
- Day 6: [tex]\( 384,000 \times 2 = 768,000 \)[/tex] bacteria

4. Conclusion:
- After 6 days, the number of bacteria in the culture is 768,000.

Thus, the correct answer is:
768,000 bacteria.
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