Solve the Problem $$\mathrm { R } = 4 \mathrm { e } ^ { \mathrm { kx } }$$

Short Answer

Solve the problem.
-The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as a percent) of having an
accident while driving a car can be modeled by the equation $$\mathrm { R } = 4 \mathrm { e } ^ { \mathrm { kx } }$$ where x is the variable concentration of alcohol in the blood and k is a constant.
(a) Suppose that a concentration of alcohol in the blood of 0.09 results in a 14% risk (R = 14) of an accident. Find the
constant k in the equation.
(b) Using this value of k, what is the risk if the concentration is 0.014?
(c) Using the same value of k, what concentration of alcohol corresponds to a risk of 100%?
(d) If the law asserts that anyone with a risk of having an accident of 12 or more should not have driving privileges,
at what concentration of alcohol in the blood should a driver be arrested and charged with a DUI?