Chapter 4.4, Problem 135AYU

Alcohol and Driving The concentration of alcohol in a person’s bloodstream is measurable. Suppose that the relative risk $R$ of having an accident while driving a car can be modelled by an equation of the form

$R=e^{kx}$

where $x$ is the percent concentration of alcohol in the bloodstream and $k$ is a constant.

Suppose that a concentration of alcohol in the bloodstream of $0.03$ percent results in a relative risk of an accident of $\mathrm{1.4.}$ Find the constant $k$ in the equation.

Using this value of $k,$ what is the relative risk if the concentration is $0.17$ percent $?$

Using the same value of $k,$ what concentration of alcohol corresponds to a relative risk of $100?$

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 a $DUI?$

Compare this situation with that of Example $10.$ If you were a lawmaker, which situation would you support $?$ Give your reasons.