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 modeled by an equation of the form, R = e k x where x is the percent 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 this value of k , what is the relative risk if the concentration is 0.17 percent? c. Using the same value of k , what concentration of alcohol corresponds to a relative risk of 100? d. 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 DU I? e. Compare this situation with that of Example 10. If you were a lawmaker, which situation would you support? Give your reasons.
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 modeled by an equation of the form, R = e k x where x is the percent 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 this value of k , what is the relative risk if the concentration is 0.17 percent? c. Using the same value of k , what concentration of alcohol corresponds to a relative risk of 100? d. 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 DU I? e. Compare this situation with that of Example 10. If you were a lawmaker, which situation would you support? Give your reasons.
Alcohol and Driving 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 an equation of the form,
where
is the percent concentration of alcohol in the bloodstream and
is a constant.
a. Suppose that a concentration of alcohol in the bloodstream of
percent results in a relative risk of an accident of
. Find the constant
in the equation.
b. Using this value of
, what is the relative risk if the concentration is
percent?
c. Using the same value of
, what concentration of alcohol corresponds to a relative risk of 100?
d. 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 DU I?
e. Compare this situation with that of Example 10. If you were a lawmaker, which situation would you support? Give your reasons.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 5 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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