Blood Alcohol Concentration - Typical Effects of the Alcohol  Consumption - Science and Maths Assignment Help

Assignment Task : 

Context 

Metabolism is the body's process of converting ingested substances into other  compounds. Metabolism results in some substances, such as alcohol, becoming less  toxic than what was originally ingested. During metabolism, alcohol is detoxified and  removed from the blood and until all of the alcohol consumed has been metabolized, it  is distributed throughout the body, affecting the brain and other tissues.  

Blood Alcohol Concentration (BAC) is an indication of the amount of alcohol in the  individual's bloodstream. To calculate BAC, the amount of alcohol in the bloodstream is  measured in milligrams (mg) of alcohol per 100 millilitres (ml) of blood. It is then  expressed in grams per 100 mL and written as a percentage such as 0.08% or 0.15%.  For example, a BAC of 0.08% means that an individual’s blood supply contains 0.08  grams (80 milligrams) of alcohol for every 100 mL blood. 

A Surge Function may be used to model the Blood Alcohol Concentration in the  bloodstream of an adult. A Surge Function, B(t), with positive real numbers A and b as  parameters is of the form: 

where t = time in minutes after the alcohol was ingested and 

 B(t) = blood alcohol concentration in mg/100 mL  

The concentration of alcohol in the brain is difficult to measure and the effects of alcohol  on an individual are calculated indirectly by noting the physical and mental impairments  that typically arise at various levels of blood alcohol concentration. Typical effects such  as impaired judgement, lowered alertness, reduced muscle coordination and altered  mood can commence with a Blood Alcohol Concentration of 0.02% and in most  countries there is a general alcohol legal limit for an "open" licence holder to drive a  motor vehicle. By studying and understanding alcohol metabolism, we can learn how  the body can dispose of alcohol and discern some of the factors that influence this  process.  

Task 

The individual data table supplied (as an attachment) shows the values of Blood  Alcohol Concentration (BAC) recorded over time for an individual after consuming one  standard drink. A standard drink in Australia is one that contains a fixed amount of  alcohol. A value of 27 in the data table indicates that the individual's Blood Alcohol  Concentration was 27 milligrams of alcohol per 100 mL of blood which equates to a  BAC of 0.027%. 

Write an investigative report that discusses the suitability of using a surge function to  model the Blood Alcohol Concentration of the individual over time. Investigate and  

discuss relevant features and critical points of the model obtained and also for the 

Mathematical Methods  

discuss relevant features and critical points of the model obtained and also for the  model for the rate of change of the BAC over time. You will also be required to  determine a model for the individual's BAC over time following the ingestion of two  additional drinks consumed at 20 minute intervals after the initial drink. 

The report should investigate the timing of the onset of typical effects of the alcohol  consumption and the amount of time that the individual will be above the Australian  general alcohol legal limit during and after consumption of the three drinks. The report  should also refine the model to determine the amount of time that the consumption of  the second and/or third drinks should be delayed to ensure the individual's BAC does  not go above the maximum Blood Alcohol Concentration legal limit.  

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