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

question 377

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?

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Definitions:

Tibial

Pertaining to the tibia, the larger and stronger of the two bones in the lower leg.

Jugular

Pertaining to the neck or throat, often in reference to the jugular vein, a major vein that carries blood back to the heart from the head.

Tachycardia

A condition characterized by an abnormally rapid heart rate, often defined as a resting heart rate above 100 beats per minute.

Systole

The phase of the heartbeat when the heart muscle contracts and pumps blood from the chambers into the arteries.