Intermediate Algebra (11th edition)

Solve each problem.

55.The average number of vehicles waiting in
line to enter a parking area is modeled by the
function defined by

,

where xis a quantity between 0 and 1 known

as the traffic intensity.(Source:Mannering,

F., and W. Kilareski, Principles of Highway

Engineering and Traffic Control,John Wiley

and Sons.) For each traffic intensity, find the

average number of vehicles waiting (to the

nearest tenth).

(a)0.1 (b)0.8 (c)0.9

(d)What happens to waiting time as traffic intensity increases?

56.The percent of deaths caused by smoking is modeled by the rational function defined by

,

where xis the number of times a smoker is more likely to die of lung cancer than a

nonsmoker is. This is called the incidence rate.(Source:Walker, A., Observation and

Inference: An Introduction to the Methods of Epidemiology,Epidemiology Resources Inc.)

For example, means that a smoker is 10 times more likely than a nonsmoker to die

of lung cancer.

(a)Find if xis 10.

(b)For what values of xis? (Hint:Change 80% to a decimal.)

(c) Can the incidence rate equal 0? Explain.

57.The force required to keep a 2000-lb car going
30 mph from skidding on a curve, where ris the
radius of the curve in feet, is given by

(a)What radius must a curve have if a force of

450 lb is needed to keep the car from skidding?

(b)As the radius of the curve is lengthened, how is

the force affected?

58.The amount of heating oil produced (in gallons per
day) by an oil refinery is modeled by the rational
function defined by

where xis the amount of gasoline produced (in hun-

dreds of gallons per day). Suppose the refinery must

produce 300 gal of heating oil per day to meet the

needs of its customers.

(a)How much gasoline will be produced per day?

(b)The graph of ƒ is shown in the figure. Use it to decide what happens to the amount

of gasoline 1 x 2 produced as the amount of heating oil 1 y 2 produced increases.

ƒ 1 x 2 =

125,000- 25 x

125 + 2 x

,

F 1 r 2 =

225,000

r

.

p 1 x 2 =80%

p 1 x 2

x= 10

p 1 x 2 =

x- 1

x

w 1 x 2 =

x^2

211 - x 2

SECTION 7.4 Equations with Rational Expressions and Graphs 393

r

F

y

x

500

400

300

200

100

0 200 400 600 800 1000

f(x) =125,000 – 25125 + 2xx