Calculating Bacterial Viable Cell Count (CFU/mL)

This problem requires calculating the viable cell concentration in a bacterial culture using data from a plate count assay.

Step 1: Understand the Data Provided

• Colonies counted on the plate: 20 CFU
• Volume of sample plated: $50 \, \mu \text{L}$
• Dilution factor of the sample: 100

Step 2: Convert Volume to Milliliters

The final count needs to be in CFU per mL ($\text{mL}^{-1}$), so convert the plated volume from microliters ($\mu \text{L}$) to milliliters ($\text{mL}$).

$ 50 \, \mu \text{L} = 50 \times 10^{-3} \, \text{mL} = 0.05 \, \text{mL} $

Step 3: Calculate Initial Cell Concentration per mL

Use the formula for viable cell count:

$ \text{Viable Cell Count (CFU/mL)} = \frac{\text{Number of Colonies Counted}}{\text{Volume Plated (mL)}} \times \text{Dilution Factor} $

Substitute the given values into the formula:

$ \text{Viable Cell Count} = \frac{20 \, \text{CFU}}{0.05 \, \text{mL}} \times 100 $

Step 4: Perform the Calculation

First, calculate the concentration in the plated volume:

$ \frac{20 \, \text{CFU}}{0.05 \, \text{mL}} = 400 \, \text{CFU/mL} $

Now, multiply by the dilution factor to get the count in the original culture:

$ 400 \, \text{CFU/mL} \times 100 = 40000 \, \text{CFU/mL} $

Conclusion

The viable cell count of the bacterial culture is 40,000 $\text{CFU mL}^{-1}$.