Math 326, April 16 -
Blood Alcohol Content
We model the progress of Blood Alcohol Content (BAC) over the
course of an evening. BAC can be estimated by taking the amount
of alcohol in the body, divided by the mass of water in the body.
We also need to account for the rate at which the body metabolizes
alcohol.
Assumptions
- The average male has water mass equal to 0.58*(Total Body Mass),
the average female has water mass equal to 0.49*(Total Body Mass).
- The average person metabolizes alcohol at a rate of 10g/hour.
- No time delay between ingestion and alcohol entering the
system. 100% of alcohol ingested enters the system (perhaps
closer to 90% in reality).
- Average drink contains 12g of alcohol.
Build a model which estimates BAC over the course of an evening, in
time increments of minutes. Inputs include how often one gets a
drink. Graph BAC along with
the levels for DUI (0.08%), losing consciousness (0.30%) and alcohol
poisoning (0.45%).
Additional Questions
- Have Excel output the number of drinks before one reaches the
"Pass out" and "Hospital" levels.
- Introduce a "cut-off" level, a limit on the number of drinks one
takes. How long does it take to get back below DUI levels, or to
sober up completely (BAC=0)?
- Alter the model so that instead of metabolizing 10g/hour, your body
metabolizes 30% of the total alcohol per hour (or 0.5%/minute).