GLEN-GRAPH & FUNCTIONS Flashcards by Fer Angelie Kaye Tripoli

Geography A global positioning system, GPS, uses satellites to allow a user
to determine his or her position on Earth.position. Radio
waves travel through air at a speed of 299,792,458 meters per second. Thus,
the function d(t)= 299,792,458t.n
A. Find the distance a sound wave will travel in 0.05, 0.2, 1.4, and 5.9 second

ANS: 14,989,622.9 m; 59,958,491.6 m; 419,709,441.2 m

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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?

ANS: 23,983,396.64 m

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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

ANS: $3750

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Archaeology Archaeologists use bones and other artifacts found at historical
sites to study a culture.determine the height of the person from a tibia bone.

A. Write two ordered pairs that represent the function.

ANS: (38.500, 173), (44.125, 188)

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B. Determine the slope of the line through the two points.

2.667

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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?

ANS: 0.4 ohm

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B. Find the voltage that the battery would produce when the current is 25.0
amperes.

ANS: 2.4 volts

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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.

ANS: 1/4

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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.

A. Find the zero of the function

ANS: 36

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B. Find the slope of the function.

ANS: -290

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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…

A. Suppose a nation’s disposable income, x,and personal consumption
expenditures, y, are shown in the table at the right. Find the MPC.

ANS: 0.86

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B. If disposable income were to increase $1805 in a year, how many additional
dollars would the average family spend?

ANS: $1552.30

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C. The marginal propensity to save, MPS, is 1-MPC. Find the MPS.

ANS: 0.14

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D. If disposable income were to increase $1805 in a year, how many additional
dollars would the average family save?

ANS: $252.70

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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.

ANS: d(p) = 0.88p

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B. Write a function for the price after the rebate r(d) if d represents the
discounted price.

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C. Use composition of functions to write a function to relate the selling price to
the original price of a computer.

ANS: r(p) = 0.88p-100

D. Find the selling prices of computers with original prices of $799.99, $999.99,
and $1499.99.

ANS: $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. Write an equation for the time t to acclimate to an altitude of f feet.

ANS: t = 2+ (x-7000)/(2000)

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.

ANS: y = 9/7 x + 16/7

B. Model J’s city mileage is 19 mpg. Use your equation to predict its highway
mileage.

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.

ANS: $6111 billion

Accounting The income tax brackets for the District of Columbia are listed
in the tax table.Alicia Davis lives in the District of Columbia. In which tax bracket is Ms. Davis
if she made $36,000 last year?

ANS: 9.5%

Transportation The table shows the percent of workers in different cities who use public transportation to get to work.

What is the correlation value?

ANS: y= 0.0000136x+4.55, r= 0.68

14. Retail Winston bought a sweater that was on sale 25% off. The original price of the sweater was $59.99.

ANS: $ 47.92

1. The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by 𝑃(𝑥) = −0.78𝑥4 + 133𝑥3 − 7500 𝑥2 + 147,500𝑥+1,440,000, where P(x) represents the population and x represents the number of years since 1890. A. Use the model to predict the population in 1980.

ANS: -253,800

B. According to this model, what happens between 1970 and 1980?

ANS: The population becomes 0

2. A doctor tells Masa to take 60 milligrams of medication each morning for three days. A. Write an equation to model this situation

ANS: 37.44 = 60𝑥³ + 60𝑥²+ 60𝑥

B. Write the related function for the equation

ANS: 𝑓(𝑥) = 60𝑥³ + 60𝑥²+ 60𝑥 − 37.44

C. Estimate the absorption rate.

ANS: About 1/2

D. Find the absorption rate of the medication.

ANS: 0.4

3. In the early 1900s, the deer population of the Kaibab Plateau in Arizona experienced a rapid increase because hunters had reduced the number of natural predators. A. Use the model to determine the population in 1905.

ANS: 4000 deers

B. Use the model to determine the population in 1920.

ANS: 67281 deers

C. According to this model, when did the deer population become zero

ANS: 1930

4. The regression equation for a set of data is y = -3.54x - 7107.7, . Use the equation to predict the number of students assigned to each adviser in the year 2005.

ANS: 10 student

5. The percent of the United States population living in metropolitan areas has increased since 1950. A. Use the model to predict the percent of the population that will be living in metropolitan areas in 2010.

ANS: 87.1%

B. Use the model to predict what year will have 85% of the population living in metropolitan areas.

ANS: 2006

The United States Census Bureau has projected the median age of the U.S. population to the year 2080. A. Use the model to predict what age the fast-food chain should target in the year 2005.

ANS: 36

B. Use the model to predict what age the fast-food chain should target in the year 2025.

ANS: 38

6. The attendance at major league baseball games for various years is listed below. Use the model to predict when the attendance will reach 71 million again.

ANS: 2000

7. Luisa Diaz is planning to build a new factory for her business.In the model 𝑃(𝑥) = 18 + 92𝑥 − 2𝑥2, P is Ms. Diaz’s monthly profit, and x is the number of employees needed to staff the new facility. A. How many employees should she hire to maximize profits?

ANS: 23 employees

B. What is her maximum profit?

ANS: $1076