580
Chapter 5 | Integration
245. [T] The following table provides hypothetical data regarding the level of service for a certain highway. Highway Speed Range (mph) Vehicles per Hour per Lane Density Range (vehicles/ mi)
242. A motor vehicle has a maximum efficiency of 33 mpg at a cruising speed of 40 mph. The efficiency drops at a rate of 0.1 mpg/mph between 40 mph and 50 mph, and at a rate of 0.4 mpg/mph between 50 mph and 80 mph. What is the efficiency in miles per gallon if the car is cruising at 50 mph? What is the efficiency in miles per gallon if the car is cruising at 80 mph? If gasoline costs $3.50/gal, what is the cost of fuel to drive 50 mi at 40 mph, at 50 mph, and at 80 mph? 243. Although some engines are more efficient at given a horsepower than others, on average, fuel efficiency decreases with horsepower at a rate of 1/25 mpg/ horsepower. If a typical 50-horsepower engine has an average fuel efficiency of 32 mpg, what is the average fuel efficiency of an engine with the following horsepower: 150, 300, 450? 244. [T] The following table lists the 2013 schedule of federal income tax versus taxable income. Taxable Income Range The Tax Is … … Of the Amount Over
> 60
< 600
< 10
60–57
600–1000
10–20
57–54
1000–1500
20–30
54–46
1500–1900
30–45
1900 – 2100
46–30
45–70
<30
Unstable
70–200
Table 5.10 a. Plot vehicles per hour per lane on the x -axis and highway speed on the y -axis. b. Compute the average decrease in speed (in miles per hour) per unit increase in congestion (vehicles per hour per lane) as the latter increases from 600 to 1000, from 1000 to 1500, and from 1500 to 2100. Does the decrease in miles per hour depend linearly on the increase in vehicles per hour per lane? c. Plot minutes per mile (60 times the reciprocal of miles per hour) as a function of vehicles per hour per lane. Is this function linear? For the next two exercises use the data in the following table, which displays bald eagle populations from 1963 to 2000 in the continental United States.
$0–$8925
10%
$0
$892.50 + 15%
$8925–$36,250
$8925
$4,991.25 + 25%
$36,250–$87,850
$36,250
$17,891.25 + 28%
$87,850–$183,250
$87,850
$44,603.25 + 33%
$183,250–$398,350
$183,250
$115,586.25 + 35%
$398,350–$400,000
$398,350
$116,163.75 + 39.6%
> $400,000
$400,000
Table 5.9 Federal Income Tax Versus Taxable Income Source : http://www.irs.gov/pub/irs-prior/ i1040tt--2013.pdf. Suppose that Steve just received a $10,000 raise. How much of this raise is left after federal taxes if Steve’s salary before receiving the raise was $40,000? If it was $90,000? If it was $385,000?
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
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