Cootie Bacteria divide every 30 minutes. At 5:00 pm, Cootie had one Cootie bacteria in her bowl. How many Cootie bacteria does she have in her bowl at 7:30 pm?
Understand the Problem
The question is asking how many Cootie bacteria will be present in a bowl at 7:30 pm, given that they divide every 30 minutes starting from one bacterium at 5:00 pm. This involves calculating the total number of divisions that occur within the specified time frame and applying that to find the total count.
Answer
The total number of Cootie bacteria at 7:30 pm is $32$.
Answer for screen readers
The total number of Cootie bacteria at 7:30 pm is $32$.
Steps to Solve
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Calculate the time difference
From 5:00 pm to 7:30 pm,
- The total time is 2 hours and 30 minutes.
- Convert this into minutes: ( 2 \times 60 + 30 = 150 ) minutes.
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Determine the number of divisions
Since the bacteria divide every 30 minutes, divide the total minutes by 30: [ \text{Number of divisions} = \frac{150}{30} = 5 ]
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Calculate the total number of bacteria
The number of bacteria doubles with each division. Starting with 1 bacterium, the total after ( n ) divisions is given by: [ \text{Total bacteria} = 1 \times 2^n ] Substituting ( n = 5 ): [ \text{Total bacteria} = 1 \times 2^5 = 32 ]
The total number of Cootie bacteria at 7:30 pm is $32$.
More Information
Cootie bacteria grow exponentially through binary fission, which is the process of dividing into two. With each 30-minute interval, the number of bacteria doubles.
Tips
- Forgetting to convert hours into minutes when calculating total time.
- Not recognizing that the division results in exponential growth, leading to underestimating the final count.
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