3.	Calculate the BAC to the nearest thousandth for a 135-lb woman who, in 3 hr, has consumed three 12-oz beers (36 oz), each having a 4.0% alcohol content. [3 marks]

(Modeling) Blood Alcohol Concentration The blood alcohol concentration (BAC) of a person who has been drinking is approximated by the following formula.

BAC = number of oz × % alcohol × 0.075 ÷ body wt in lb − hr of drinking × 0.015

To calculate the Blood Alcohol Concentration (BAC) for the 135-lb woman, we'll use the provided formula:

\[
\text{BAC} = \frac{\text{number of oz} \times \% \text{ alcohol} \times 0.075}{\text{body weight in lb}} - \text{hours of drinking} \times 0.015
\]

Given:
- Number of ounces consumed = \(36 \, \text{oz}\)
- Percentage of alcohol = \(4.0\%\) (or \(0.04\) as a decimal)
- Body weight = \(135 \, \text{lb}\)
- Hours of drinking = \(3 \, \text{hours}\)

### Step 1: Calculate the alcohol contribution to BAC
\[
\text{Alcohol Contribution} = \frac{36 \times 0.04 \times 0.075}{135}
\]
\[
\text{Alcohol Contribution} = \frac{0.108}{135} = 0.0008
\]

### Step 2: Calculate the reduction due to time
\[
\text{Reduction Due to Time} = 3 \times 0.015 = 0.045
\]

### Step 3: Calculate the final BAC
\[
\text{BAC} = 0.0008 - 0.045 = -0.0442
\]

Since BAC cannot be negative, it should be considered 0 in practical terms, but mathematically:
\[
\text{BAC} = 0 \, \text{(since negative BAC doesn't make physical sense)}
\]

However, let's recompute more carefully to make sure we didn't make any mistakes:

### Recalculation:
1. Compute the BAC contribution from the alcohol consumed:
   \[
   \text{BAC} = \frac{36 \times 0.04 \times 0.075}{135}
   \]
   \[
   \text{BAC} = \frac{0.108}{135} = 0.0008
   \]
2. Subtract the reduction due to the time of drinking:
   \[
   \text{BAC} = 0.0008 - 0.045 = -0.0442
   \]

After rechecking, this negative value still persists. Since BAC can't be negative, the BAC would be effectively 0.

### Final Answer:
The BAC for the woman is approximately **0.000** (which rounds to 0.000 to the nearest thousandth).

Would you like any more details or clarifications?

Here are some related questions:
1. How does body weight affect BAC?
2. How is alcohol percentage in drinks calculated?
3. What other factors might influence BAC aside from weight and time?
4. Why does BAC decrease over time?
5. What are the legal limits for BAC in different countries?

**Tip:** Always recheck BAC calculations to ensure accuracy, especially when dealing with time reductions.

Learn how to calculate Blood Alcohol Concentration (BAC) for a 135-lb woman who consumed three 12-oz beers (36 oz total), each with 4.0% alcohol content over a period of 3 hours. Follow a step-by-step solution and understand the effects of alcohol consumption on BAC.

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