Answer :
To determine the number of E. coli cells in the culture after two hours, we need to consider the following information:
1. Initial number of cells: 10,000
2. Generation time: 30 minutes
3. Total time for growth: 2 hours, which is equivalent to 120 minutes
Now, let's break down the process step-by-step:
1. Calculate the number of generations:
Since the generation time is 30 minutes, we need to see how many 30-minute intervals fit into 120 minutes.
[tex]\[
\text{Number of generations} = \frac{120 \text{ minutes}}{30 \text{ minutes/generation}} = 4 \text{ generations}
\][/tex]
2. Calculate the final number of cells:
E. coli cells divide and double their number every generation. So, if you have a certain number of cells [tex]\(C\)[/tex] that divide over [tex]\(n\)[/tex] generations, the formula to find the final number of cells is:
[tex]\[
\text{Final number of cells} = \text{Initial number of cells} \times (2^n)
\][/tex]
Here, the initial number of cells is 10,000, and the number of generations is 4. So:
[tex]\[
\text{Final number of cells} = 10,000 \times (2^4)
\][/tex]
[tex]\[
\text{Final number of cells} = 10,000 \times 16 = 160,000
\][/tex]
Thus, after two hours, the culture will have 160,000 E. coli cells. Therefore, the correct answer is 160,000.
1. Initial number of cells: 10,000
2. Generation time: 30 minutes
3. Total time for growth: 2 hours, which is equivalent to 120 minutes
Now, let's break down the process step-by-step:
1. Calculate the number of generations:
Since the generation time is 30 minutes, we need to see how many 30-minute intervals fit into 120 minutes.
[tex]\[
\text{Number of generations} = \frac{120 \text{ minutes}}{30 \text{ minutes/generation}} = 4 \text{ generations}
\][/tex]
2. Calculate the final number of cells:
E. coli cells divide and double their number every generation. So, if you have a certain number of cells [tex]\(C\)[/tex] that divide over [tex]\(n\)[/tex] generations, the formula to find the final number of cells is:
[tex]\[
\text{Final number of cells} = \text{Initial number of cells} \times (2^n)
\][/tex]
Here, the initial number of cells is 10,000, and the number of generations is 4. So:
[tex]\[
\text{Final number of cells} = 10,000 \times (2^4)
\][/tex]
[tex]\[
\text{Final number of cells} = 10,000 \times 16 = 160,000
\][/tex]
Thus, after two hours, the culture will have 160,000 E. coli cells. Therefore, the correct answer is 160,000.
