GRAPH PLOTTING (LINEAR) Flashcards
Geography A global positioning system, GPS, uses satellites to allow a user to determine his or her position on Earth. The system depends on satellite signals that are reflected to and from a hand-held transmitter. The time that the signal takes to reflect is used to determine the transmitter’s position. Radio waves travel through air at a speed of 299,792,458 meters per second. Thus, the function d(t)= 299,792,458t relates the time t in seconds to the distance traveled d(t) in meters.
A. Find the distance a sound wave will travel in 0.05, 0.2, 1.4, and 5.9 seconds.
A) ANS: 14,989,622.9 m; 59,958,491.6 m; 419,709,441.2 m
Geography A global positioning system, GPS, uses satellites to allow a user to determine his or her position on Earth. The system depends on satellite signals that are reflected to and from a hand-held transmitter. The time that the signal takes to reflect is used to determine the transmitter’s position. Radio waves travel through air at a speed of 299,792,458 meters per second. Thus, the function d(t)= 299,792,458t relates the time t in seconds to the distance traveled d(t) in meters.
B. If a signal from a GPS satellite is received at a transmitter in 0.08 seconds, how far from the transmitter is the satellite?
B) ANS: 23,983,396.64 m
Finance A sales representative for a cosmetics supplier is paid an annual salary plus a bonus of 3% of her sales over $275,000. Let f(x) = x-275,000 and h(x)= 0.03x. Find her bonus if her sales for the year are $400,000.
$3750
Archaeology Archaeologists use bones and other artifacts found at historical sites to study a culture. One analysis they perform is to use a function to determine the height of the person from a tibia bone. Typically a man whose tibia is 38.500 centimeters long is 173 centimeters tall. A man with a 44.125 centimeter tibia is 188 centimeters tall.
A. Write two ordered pairs that represent the function.
A) ANS: (38.500, 173), (44.125, 188)
Archaeology Archaeologists use bones and other artifacts found at historical sites to study a culture. One analysis they perform is to use a function to determine the height of the person from a tibia bone. Typically a man whose tibia is 38.500 centimeters long is 173 centimeters tall. A man with a 44.125 centimeter tibia is 188 centimeters tall.
B. Determine the slope of the line through the two points.
B) ANS: 2.667
Electronics The voltage V in volts produced by a battery is a linear function of the current i in amperes drawn from it. The opposite of the slope of the line represents the battery’s effective resistance R in ohms. For a certain battery, V=12.0 when i=1.0 and V= 8.4 when i=10.0.
A. What is the effective resistance of the battery?
A) ANS: 0.4 ohm
Electronics The voltage V in volts produced by a battery is a linear function of the current i in amperes drawn from it. The opposite of the slope of the line represents the battery’s effective resistance R in ohms. For a certain battery, V=12.0 when i=1.0 and V= 8.4 when i=10.0.
B. Find the voltage that the battery would produce when the current is 25.0 amperes.
B) ANS: 2.4 volts
Chemistry According to Charles’ Law, the pressure P in pascals of a fixed volume of a gas is linearly related to the temperature T in degrees Celsius. In an experiment, it was found that when T=40, P=90 and when T=80, P=100. What is the slope of the line containing these points?
1/4
Accounting A business’s capital costs are expenses for things that last more than one year and lose value or wear out over time. Examples include equipment, buildings, and patents. The value of these items declines, or depreciates over time. One way to calculate depreciation is the straight-line method, using the value and the estimated life of the asset. Suppose v(t)=10,440-290t describes the value v(t) of a piece of software after t months.
A) Find the zero of the function
B) Find the slope of the function
A) 36
b) -290
Economics Economists call the relationship between a nation’s disposable income and personal consumption expenditures the marginal propensity to consume or MPC. An MPC of 0.7 means that for each $1 increase in disposable income, consumption increases $0.70. That is, 70% of each additional dollar earned is spent and 30% is saved.
x
56
76
y
50
67.2
A. Suppose a nation’s disposable income, x,and personal consumption expenditures, y, are shown in the table at the right. Find the MPC.
A) 0.86
Economics Economists call the relationship between a nation’s disposable income and personal consumption expenditures the marginal propensity to consume or MPC. An MPC of 0.7 means that for each $1 increase in disposable income, consumption increases $0.70. That is, 70% of each additional dollar earned is spent and 30% is saved.
x
56
76
y
50
67.2
B. If disposable income were to increase $1805 in a year, how many additional dollars would the average family spend?
B) $1552.30
Economics Economists call the relationship between a nation’s disposable income and personal consumption expenditures the marginal propensity to consume or MPC. An MPC of 0.7 means that for each $1 increase in disposable income, consumption increases $0.70. That is, 70% of each additional dollar earned is spent and 30% is saved.
x
56
76
y
50
67.2
C. The marginal propensity to save, MPS, is 1-MPC. Find the MPS.
C) 0.14
Economics Economists call the relationship between a nation’s disposable income and personal consumption expenditures the marginal propensity to consume or MPC. An MPC of 0.7 means that for each $1 increase in disposable income, consumption increases $0.70. That is, 70% of each additional dollar earned is spent and 30% is saved.
x
56
76
y
50
67.2
A. Suppose a nation’s disposable income, x,and personal consumption expenditures, y, are shown in the table at the right. Find the MPC.
B. If disposable income were to increase $1805 in a year, how many additional dollars would the average family spend?
C. The marginal propensity to save, MPS, is 1-MPC. Find the MPS.
D. If disposable income were to increase $1805 in a year, how many additional dollars would the average family save?
A) 0.86
B) $1552.30
C) 0.14
D) $252.7
Computer Depot offers a 12% discount on computers sold Labor Day weekend. There is also a $100 rebate available.
A. Write a function for the price after the discount d(p) if p represents the original price of a computer.
B. Write a function for the price after the rebate r(d) if d represents the discounted price.
C. Use composition of functions to write a function to relate the selling price to the original price of a computer.
D. Find the selling prices of computers with original prices of $799.99, $999.99, and $1499.99.
A) d(p) = 0.88p
B) r(d) = d - 100
C) r(p) = 0.88p-100
D) $603.99,$779.99, $1219.99
Sports Skiers, hikers, and climbers often experience altitude sickness as they reach elevations of 8000 feet and more. A good rule of thumb for the amount of time that it takes to become acclimated to high elevations is 2 weeks for the first 7000 feet. After that, it will take 1 week more for each additional 2000 feet of altitude.
A) Write an equation for the time t to acclimate to an altitude of f feet
B) Mt. Whitney in California is the highest peak in the contiguous 48 states. It is located in Eastern Sierra Nevada, on the border between Sequoia National Park and Inyo National Forest. About how many weeks would it take a person to acclimate to Mt. Whitney’s elevation of 14,494 feet?
A) I=2+(x-7000)/2000
B) 5.7 weeks
Transportation The mileage in miles per gallon (mpg) for city and highway driving of several 1999 models are given in the chart.
A. Find a linear equation that can be used to find a car’s highway mileage based on its city mileage.
B. Model J’s city mileage is 19 mpg. Use your equation to predict its highway
mileage.
A) ANS: y = 9/7 x + 16/7
B) ANS: 26.7 mpg
Business In 1995, retail sales of apparel in the United States were $70,583 billion. Apparel sales were $82,805 billion in 1997. Assuming a linear relationship, find the average annual rate of increase.
$6111 billion
Accounting The income tax brackets for the District of Columbia are listed in the tax table.
BASTA NAAY TABLE
Alicia Davis lives in the District of Columbia. In which tax bracket is Ms. Davis if she made $36,000 last year?
9.5%
Transportation The table shows the percent of workers in different cities who use public transportation to get to work.
BASTA NAAY TABLE
What is the correlation value?
y= 0.0000136x+4.55, r= 0.68
Retail Winston bought a sweater that was on sale 25% off. The original
price of the sweater was $59.99. If sales tax in Winston’s area is 6.5%, how
much did the sweater cost including sale tax?
TABLE NAPUD
$47.92
