lcohol and Driving The concentration of alcohol in a person’s bloodstream is measurable.

Question

Suppose that the relative risk R 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 a DUI?

Answer 1

ignoring e for this, because it seems like well maybe there was a typo?

(a) 0.03% k = 1.4

3/100000 * k = 1.4

k = 46666 2/3

if you meant 3%, then we get 46 2/3 as k

(b)R = 100 = kx

100 = kx

100 = 46 2/3 x => x = 2.142857143....

(or 100= 46666 2/3 x = 0.002142857....)

(c) I guess k would equal 46 2/3?, tell me your thoughts.

Anyways, then 5 = 46 2/3 x,

so x = 0.107142857

Did you mean e as in the mathematical constant? (Euler's number)

Like, the number e is an important mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm. It is the limit of (1 + 1/n)n as n approaches infinity.

Thanks if you have any additions to make or observations tell me