5. Peyton is a 130-pound female who attended a wedding at a fancy hotel.She began drinking at 7 pm After finishing her 4^th glass of wine at 10 pm, she left, driving her own car. She was pulled over about a mile from her home. What was her BAC at the time she was pulled over?

To determine Peyton's Blood Alcohol Content (BAC) at the time she was pulled over, we need to consider several factors, including her weight, the amount of alcohol consumed, the time elapsed since drinking, and her gender. For simplicity, we'll use the Widmark formula, which is commonly used to estimate BAC:<br /><br />\[ \text{BAC} = \frac{\text{Alcohol Consumed (grams)}}{\text{Body Weight (grams)}} \times \text{Rational Factor} \times \text{Time Factor} \]<br /><br />1. **Convert the number of drinks to grams of alcohol:**<br /> - Each standard drink contains approximately 14 grams of pure alcohol.<br /> - Peyton had 4 drinks: \( 4 \times 14 = 56 \) grams of alcohol.<br /><br />2. **Convert body weight to grams:**<br /> - Peyton's weight is 130 pounds. Since 1 pound is approximately 453.592 grams:<br /> \[ 130 \text{ pounds} \times 453.592 \text{ grams/pound} = 58927.76 \text{ grams} \]<br /><br />3. **Rational Factor:**<br /> - For females, the rational factor is approximately 0.66.<br /><br />4. **Time Factor:**<br /> - The time elapsed since drinking is 3 hours (from 7 pm to 10 pm).<br /> - The time factor for alcohol elimination is approximately 0.015 per hour for females.<br /><br />Now, plug these values into the formula:<br /><br />\[ \text{BAC} = \frac{56 \text{ grams}}{58927.76 \text{ grams}} \times 0.66 \times (1 - 0.015 \times 3) \]<br /><br />First, calculate the fraction:<br /><br />\[ \frac{56}{58927.76} \approx 0.000952 \]<br /><br />Then, apply the rational factor and time factor:<br /><br />\[ \text{BAC} = 0.000952 \times 0.66 \times (1 - 0.045) \]<br />\[ \text{BAC} = 0.000952 \times 0.66 \times 0.955 \]<br />\[ \text{BAC} \approx 0.000617 \]<br /><br />Finally, convert this to a percentage:<br /><br />\[ \text{BAC} \approx 0.0617\% \]<br /><br />So, Peyton's BAC at the time she was pulled over was approximately 0.0617%, which is slightly above the legal limit of 0.08% for driving in many jurisdictions.