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Sure, let's go through this step-by-step. We're asked to calculate the concentration of bacteria in the original culture using the given dilution factors and colony counts from a Standard Plate Count (SPC) method. We'll fill in the missing parts of the table and explain the concept along the way.
Here is the given information in the table form:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Dilution Factor} & \text{Number of Colonies} & \text{Bacterial Concentration in Original Culture (CFU/mL)} \\ \hline 10^0 & 10 & 10 \\ \hline 10^5 & 10 & 1,000,000 \\ \hline 10 & & \\ \hline 10 & & \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. Identify the Dilution Factors and Colony Counts:
- For [tex]\(10^0\)[/tex] dilution factor, the number of colonies is 10.
- For [tex]\(10^5\)[/tex] dilution factor, the number of colonies is 10.
2. Understand the Formula for Calculating CFU/mL:
The concentration of bacteria in the original culture (CFU/mL) can be calculated using the formula:
[tex]\[ \text{CFU/mL} = \frac{\text{Number of Colonies} \times \text{Dilution Factor}}{\text{Volume Plated (mL)}} \][/tex]
Since the volume plated is typically 1 mL (unless otherwise specified), the formula simplifies to:
[tex]\[ \text{CFU/mL} = \text{Number of Colonies} \times \text{Dilution Factor} \][/tex]
3. Calculate the Bacterial Concentration for Each Dilution:
- For the [tex]\(10^0\)[/tex] dilution:
[tex]\[ \text{CFU/mL} = 10 \times 10^0 = 10 \][/tex]
- For the [tex]\(10^5\)[/tex] dilution:
[tex]\[ \text{CFU/mL} = 10 \times 10^5 = 1,000,000 \][/tex]
4. Fill in the Table:
Using these calculations, the table is updated as:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Dilution Factor} & \text{Number of Colonies} & \text{Bacterial Concentration in Original Culture (CFU/mL)} \\ \hline 10^0 & 10 & 10 \\ \hline 10^5 & 10 & 1,000,000 \\ \hline 10 & & \\ \hline 10 & & \\ \hline \end{array} \][/tex]
### Conclusion:
From the above calculations, we find that the bacterial concentration in the original culture for a dilution factor of [tex]\(10^0\)[/tex] is 10 CFU/mL and for [tex]\(10^5\)[/tex] is 1,000,000 CFU/mL. These results can help us understand the initial concentration of bacteria before dilution.
Here is the given information in the table form:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Dilution Factor} & \text{Number of Colonies} & \text{Bacterial Concentration in Original Culture (CFU/mL)} \\ \hline 10^0 & 10 & 10 \\ \hline 10^5 & 10 & 1,000,000 \\ \hline 10 & & \\ \hline 10 & & \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. Identify the Dilution Factors and Colony Counts:
- For [tex]\(10^0\)[/tex] dilution factor, the number of colonies is 10.
- For [tex]\(10^5\)[/tex] dilution factor, the number of colonies is 10.
2. Understand the Formula for Calculating CFU/mL:
The concentration of bacteria in the original culture (CFU/mL) can be calculated using the formula:
[tex]\[ \text{CFU/mL} = \frac{\text{Number of Colonies} \times \text{Dilution Factor}}{\text{Volume Plated (mL)}} \][/tex]
Since the volume plated is typically 1 mL (unless otherwise specified), the formula simplifies to:
[tex]\[ \text{CFU/mL} = \text{Number of Colonies} \times \text{Dilution Factor} \][/tex]
3. Calculate the Bacterial Concentration for Each Dilution:
- For the [tex]\(10^0\)[/tex] dilution:
[tex]\[ \text{CFU/mL} = 10 \times 10^0 = 10 \][/tex]
- For the [tex]\(10^5\)[/tex] dilution:
[tex]\[ \text{CFU/mL} = 10 \times 10^5 = 1,000,000 \][/tex]
4. Fill in the Table:
Using these calculations, the table is updated as:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Dilution Factor} & \text{Number of Colonies} & \text{Bacterial Concentration in Original Culture (CFU/mL)} \\ \hline 10^0 & 10 & 10 \\ \hline 10^5 & 10 & 1,000,000 \\ \hline 10 & & \\ \hline 10 & & \\ \hline \end{array} \][/tex]
### Conclusion:
From the above calculations, we find that the bacterial concentration in the original culture for a dilution factor of [tex]\(10^0\)[/tex] is 10 CFU/mL and for [tex]\(10^5\)[/tex] is 1,000,000 CFU/mL. These results can help us understand the initial concentration of bacteria before dilution.
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