1) If 3 ml of culture is diluted by adding 9 ml of water, and the absorbancy reading of the diluted culture is 0.082, what is the actual absorbancy?

2) If 0.1 mls of a 10^-3 dilution of a culture is

Question

1) If 3 ml of culture is diluted by adding 9 ml of water, and the absorbancy reading of the diluted culture is 0.082, what is the actual absorbancy?

2) If 0.1 mls of a 10^-3 dilution of a culture is plated out and 65 colonies appear after incubation, how many Cfu/ml were in the undiluted culture?

VIPSolutions · Accepted Answer

Let's solve each question step by step.

---

### 1. **Absorbance Calculation after Dilution**

**Given:**
- 3 ml culture + 9 ml water = **12 ml total volume**
- Absorbance of diluted sample = **0.082**

**Step 1: Find Dilution Factor**

Dilution factor = (total volume) / (volume of culture)

$$
\text{Dilution factor} = \frac{3 + 9}{3} = \frac{12}{3} = 4
$$

So the sample was diluted **4-fold**.

**Step 2: Calculate Actual (Undiluted) Absorbance**

$$
\text{Actual Absorbance} = \text{Diluted Absorbance} \times \text{Dilution Factor}
$$
$$
= 0.082 \times 4 = 0.328
$$

**Answer:**  
**The actual absorbance of the undiluted culture is 0.328.**

---

### 2. **CFU/ml Calculation**

**Given:**
- 0.1 ml of a $10^{-3}$ dilution plated
- 65 colonies counted

**Step 1: Calculate CFU in plated volume**

The colonies counted represent the number of viable bacteria in 0.1 ml of the $10^{-3}$ dilution.

**Step 2: Find CFU per ml in the $10^{-3}$ dilution**

$$
\text{CFU/ml in } 10^{-3} \text{ dilution} = \frac{65}{0.1} = 650 \text{ CFU/ml}
$$

**Step 3: Calculate CFU/ml in original (undiluted) culture**

Because this is the $10^{-3}$ dilution:

$$
\text{CFU/ml in original} = 650 \times 10^3 = 6.5 \times 10^5 \text{ CFU/ml}
$$

**Answer:**  
**The undiluted culture had $6.5 \times 10^5$ CFU/ml.**

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**Summary:**
1. Actual absorbance = **0.328**
2. Undiluted culture = **$6.5 \times 10^5$ CFU/ml**

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