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Concentration of Alcohol and Relative Risk

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The concentration of alcohol in a person's bloodstream is measurable. Suppose that the relative risk of having an accident while driving a car can be modeled by the equation:

R = e^(kx)

Where x is the percent of concentration of alcohol in the bloodstream and k is a constant.
(a) Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.
(b) Using the same value of k, what concentration of alcohol corresponds to a relative risk of 100?
(c) If the law asserts that anyone with a relative risk of having an accident of 5 or more should not have driving privileges, at what concentration of alcohol in the bloodstream should a driver be arrested and charged with DUI?

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Solution Preview

1.a
1.4=e^(0.03k). k=ln1.4/0.03=11.22
1.b
100=e^(11.22x). x=ln100/11.22=41.04% alcohol
1.c
5=e^(11.22x). ...

Solution Summary

The solution gives detailed steps on calculating the concentration of alcohol if the equation for relative risk of an accident is given. All formula and calculations are shown and explained.

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