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

Let's correctly calculate the Blood Alcohol Concentration (BAC) using the provided formula.

### Step 1: Understand the formula
The formula for BAC is:
\[
BAC = \frac{\text{(number of oz) } \times (\% \text{ alcohol}) \times 0.075}{\text{body weight in lbs}} - (\text{hours of drinking} \times 0.015)
\]

### Step 2: Substitute the values
- Weight of the woman = 135 lbs
- Hours of drinking = 3 hours
- Amount of beer consumed = 36 oz
- Alcohol percentage = 4.0% = 0.04 (in decimal form)

### Step 3: Apply the formula
First, calculate the BAC due to alcohol consumption:
\[
BAC_{\text{alcohol}} = \frac{36 \times 0.04 \times 0.075}{135}
\]

Then subtract the reduction due to the hours of drinking:
\[
\text{BAC reduction} = 3 \times 0.015 = 0.045
\]

The final BAC is:
\[
BAC = BAC_{\text{alcohol}} - \text{BAC reduction}
\]

Now, let's calculate this accurately.# Recalculating the BAC accurately with the given formula

# Step 1: Calculate BAC due to alcohol intake
bac_due_to_alcohol = (36 * 0.04 * 0.075) / 135

# Step 2: Calculate reduction due to time
time_reduction = hours_drinking * time_reduction_rate

# Step 3: Final BAC calculation
final_bac = bac_due_to_alcohol - time_reduction

# Rounding to the nearest thousandth
round(final_bac, 3)The calculation once again results in a negative BAC, \(-0.044\). This indicates that the alcohol consumed was fully metabolized after 3 hours, which is why the formula produces a negative result. In reality, when BAC is reduced to zero, it cannot go below that value.

Thus, the final BAC should be \( 0.000 \).

Let me know if you'd like more information or if you have further questions. Here are some related questions:

1. What is the typical rate at which alcohol is metabolized?
2. How does the amount of alcohol consumed impact BAC over time?
3. Why do smaller individuals tend to have a higher BAC than larger individuals?
4. What are the health risks associated with a high BAC?
5. How does the type of alcoholic beverage affect BAC?

**Tip:** Remember, BAC cannot drop below zero. If alcohol is metabolized faster than it's consumed, your BAC will hit zero, not a negative value.

Learn how to calculate the Blood Alcohol Concentration (BAC) for a 135-lb woman who has consumed three 12-oz beers with 4.0% alcohol content over 3 hours. Detailed step-by-step solution with formulas and numerical calculations provided.

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