Putting It Together: Real Numbers and Algebraic Expressions
At the start of this module, you were presented with a formula commonly used by forensic scientists to calculate blood alcohol content:
[latex]B=-0.015t +\left(\dfrac{2.84N}{Wg}\normalsize\right)[/latex]
where
- B = percentage of BAC
- t = number of hours since the first drink
- N = number of “standard drinks” (a standard drink is one 12-ounce beer, one 5-ounce glass of wine, or one 1.5-ounce shot of liquor). N should be at least 1.
- W = weight in pounds
- g = gender constant: 0.68 for men and 0.55 for women
Remember Joan? When we left her, she was at a party. She had three drinks and then wanted to leave. This was worrisome. We posed the following questions:
- Where would she fall on the table of the progressive effects of alcohol after 1.5 hours?
- Would she be within the legal limit to drive after this amount of time?
- N = [latex]3[/latex] standard drinks
- W =[latex]135[/latex] pounds
- t =[latex]1.5[/latex] hours
- g =[latex]0.55[/latex]
[latex]\begin{array}{l}\text{B} = -0.015t +\left(\dfrac{2.84N}{Wg}\normalsize\right)\\\text{B} = -0.015(1.5) +\left(\dfrac{2.84(3)}{(135)(0.55)}\normalsize\right)\\\text{B} = -0.0225 +\left(\dfrac{8.52}{(74.25)}\normalsize\right)\\\text{B} = -0.0225 +\left(0.1147\right)\\\text{B} = 0.092\\\end{array}[/latex]
The units of B are a percentage, so in this scenario after [latex]1.5[/latex] hours and after consuming three standard drinks, Joan's BAC is [latex]0.092\%[/latex]. How is Joan doing? From the table below, we can predict that she's experiencing blunted feelings, reduced sensitivity to pain, euphoria, disinhibition, and extroversion. In addition, her reasoning, depth perception, peripheral vision, and glare recovery are probably impaired. Question 2 asks whether she would be within the legal limit to drive. If we assume that the legal limit is [latex]0.08\%[/latex], then NO, she would not be within the legal limit to drive. One of her friends should take her car keys and help her get home.Progressive effects of alcohol | ||
---|---|---|
BAC (% by vol.) | Behavior | Impairment |
[latex]0.001–0.029[/latex] |
|
|
[latex]0.030–0.059[/latex] |
|
|
[latex]0.060–0.099[/latex] |
|
|
[latex]0.100–0.199[/latex] |
|
|
[latex]0.200–0.299[/latex] |
|
|
[latex]0.300–0.399[/latex] |
|
|
[latex]0.400–0.500[/latex] |
|
|
[latex]>0.50[/latex] |
|
|
Licenses & Attributions
CC licensed content, Original
- Putting It Together: Solving Linear Equations and Inequalities. Provided by: Lumen Learning License: CC BY: Attribution.
- Screenshot: Forest. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Re: Visual Multiplication and 48/2(9+3). Authored by: Vi Hart. License: All Rights Reserved. License terms: Standard YouTube License.