### Analysis of Blood Alcohol Content Data

## by Shayna Kriss

Submitted : Fall 2010

The purpose of this project is to fit an equation for the blood concentration of alcohol (as a function of time in minutes) to a given set of experimental data. The given experimental data is various blood alcohol levels for a 75 kg subject after drinking 15 mls of 95% alcohol and is from a 1977 study. This is to be done by solving for three constants: A, k_{1} and k_{2}.There is a series of steps listed to follow. First, using knowledge of improper integrals, it must be shown that the integral of the given equation from zero to infinity equals the constant value . Secondly, the equation must be derived to determine an expression for the time at which the maximum blood alcohol concentration will occur. After deriving this expression, it must be substituted into the original equation to create an expression for the value of blood alcohol concentration at the time it occurs. Using the given experimental data the trapezoidal method is then utilized to solve for the total integral value of the original equation from zero to infinity (which is assumed to be the last data point in the experimental data). Setting these numbers equal to their respective equations gives you three equations with three unknowns; a system of equations is produced. Solving the system of equations produces the values of the constants A, k_{1}, and k_{2}. The last step of this project is to plot the given data against the model with the constant values to determine how closely the equation represents the experimental data. The final result is that the constants A, k_{1}, and k_{2} are equal to 303.38895, 0.098553, and 0.02083 respectively. The model closely follows the experimental data for five out of nine of the data points, which is over half.

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