Deck 9: Modeling Our World

Question 1

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

Answer 1

a)On a long trip, distance from home increases with time.
b)20 miles per hour.
c)Good model if speed is constant for 8 hours.

Question 2

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
(hours worked, yearly wages)

Answer 2

Answers may vary.
a)The domain of the function is the amount of hours worked per week between 10
and 60 hours and the range is yearly wages (in thousands of dollars)from $15K to
$90K.
b) c)The function should be roughly increasing. Typically the more hours someone
works, the more money they make. Any time over 40 hours, usually includes an
overtime wage which raises the overall yearly wages dramatically. However, many
people have a fixed salary regardless of how many hours they work, so this may not
represent an appropriate model.

Question 3

In the following situation, state whether two variables are related in a way that might be described by a function. If so,
identify the independent and dependent variables.
You make a list of the titles of books in a public library and their copyright year.

A)Independend variable, book title; dependent variable, copyright year
B)Independend variable, copyright year; dependent variable, book title
C)does not describe a function

Answer 3

C

Question 4

Plot and label the given points.

Question 5

In the following situation, state whether two variables are related in a way that might be described by a function. If so,
identify the independent and dependent variables.
You are taking a road trip in a car and want to know how far you've traveled (read the odometer) at various times during your trip.

A)Independend variable, distance traveled; dependent variable, time
B)Independend variable, time; dependent variable, distance traveled
C)does not describe a function

Question 6

Plot and label the given points.

Question 7

Write the word or phrase that best completes each statement or answers the question.For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
(size of truck, average fuel mileage)

Question 8

Plot and label the given points.
True or False? The rate of change is equal to the slope of the graph.

Question 9

Plot and label the given points.

Question 10

Plot and label the given points.
The population of a town with an initial population of 68,555 grows at a rate of 3.8% per year. Create an exponential function of the form Q

Question 11

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

Question 12

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

Question 13

Plot and label the given points.

Question 14

Plot and label the given points.

Question 15

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

Question 16

Provide an appropriate response.
The following graph represents a function. Identify the independent and dependent variables and describe the domain and range.

A)The independent variable is age and the dependent variable is time, measured in years. The domain is the ages between 0 and 79. The range is the years between 1980 and 2004.
B)The independent variable is time, measured in years, and the dependent variable is age. The domain is the years between 1980 and 2004. The range is the ages between 0 and 79.
C)The independent variable is age and the dependent variable is time, measured in years. The domain is the years between 1980 and 2004. The range is the ages between 0 and 79.
D)The independent variable is time, measured in years, and the dependent variable is age. The domain is the ages between 0 and 79. The range is the years between 1980 and 2004.

Question 17

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
(time spent studying, percentage on exam)

Question 18

Write an equation for the linear function and use it to answer the given question.
The Math Club plans to pay a visitor $62 to speak at a fundraiser. Tickets will be sold for $2 each. Find an equation that gives the profit/loss for the event as it varies with the number of tickets sold.
How many people must attend the event for the club to break even.

Question 19

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
(miles ran per week, 5K time)

Question 20

Plot and label the given points.

Question 21

Create the required linear function an use it to answer the question.
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 798. Based on these two
Data points, create a linear equation for the function that describes how score varies as a function of
Time.

Question 22

True or False? The demand for basketball tickets is a function of their price.

Question 23

Solve the equation for the unknown quantity x.

Question 24

Provide an appropriate response.
The general shape of an exponential growth function is a ______.

A)rising line
B)falling curve
C)falling line
D)rising curve

Question 25

Provide an appropriate response.
The population of a town with an initial population of 62,300 is decreasing at a rate of 3.2% per year. Make a graph of the exponential function.

Question 26

Provide an appropriate response.
If prices of gold decrease at a monthly rate of 0.7%, by what percentage do they decrease in a year.

A)10.1%
B)8.1%
C)8.4%
D)8.7%

Question 27

Write a short statement that expresses a possible function between the given variables.
(price of a DVD player, demand for DVD player)

A)As the price of a DVD player increases, the demand generally increases.
B)As the demand of a DVD player decreases, the price generally increases.
C)As the demand of a DVD player increases, the price generally decreases.
D)As the price of a DVD player increases, the demand generally decreases.

Question 28

Provide an appropriate response.
Between 1998 and 2002, the average rate of inflation for a particular country was about 5% per year. If a cart of groceries cost $109 in 1998, what did it cost in 2002?

A)$139.11
B)$159.59
C)$126.18
D)$132.49

Question 29

Provide an appropriate response.
True or False? A negative slope means a line falling right.

A)False
B)True

Question 30

Draw a graph of the function and use the graph to answer the question.
The cost of tuition at one community college is $400 plus $125 per credit. Graph the equation, and find the cost if a student registers for 12 credits.

Question 31

Provide an appropriate response.
The process of measuring the ages of rocks, bones, pottery, or other solid objects that contain radioactive elements is called ________.

A)doubling time
B)radioactive measuring
C)half-life
D)radioactive decay

Question 32

Provide an appropriate response.
A certain drug is eliminated from the bloodstream exponentially with a half-life of 24 hours. Suppose that a patient receives an initial dose of 15 milligrams of the drug at midnight. How much
Of the drug is in the patient's blood at noon the next day?

A)10.61 mg
B)3.75 mg
C)5.3 mg
D)0.71 mg

Question 33

Provide an appropriate response.
The given table represents a function. Identify the independent and dependent variables, and describe the domain and range.

A)The variables are (temperature, time)or (temperature, date). The domain is all temperatures between 36° and 86° and the range is all days over the course of a year.
B)The variables are (temperature, time)or (temperature, date). The domain is all temperatures between 41° and 41° and the range is all days over the course of a year.
C)The variables are (time, temperature)or (date, temperature). The domain is all days over the course of a year. The range is temperatures between 36° and 86°.
D)The variables are (time, temperature)or (date, temperature). The domain is all days over the course of a year. The range is temperatures between 41° and 41°.

Question 34

Create the required linear function an use it to answer the question.
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 780. Based on these two
Data points, create a linear equation for the function that describes how score varies as a function of
Time. Use this function to predict an average score for persons taking a 43-hour review course.
Round your answer to the tenths place.

A)664.7
B)676.2
C)672.0
D)686.0

Question 35

The given situation involves a rate of change that you may assume to be constant. Write a statement that describes howone variable varies with respect to another, give the rate of change numerically (with units), and use the rate of changerule to answer the questions.
A gas station owner finds that for every penny increase in the price of gasoline, she sells 1516 fewer gallons of gas per week. How much more or less gas will she sell if she raises the price by 10 cents
Per gallon? If she decreases the price by 2 cents per gallon?

A)At a particular gas station, sales decrease with respect to price by 1516 gallons per cent. The rate of change is 1516 gallons per cent. If the price is increased by 10 cents per gallon, the
Change in gas sales is 7580 gallons. If the price is decreased by 2 cents, gas sales increase by
-1516 gallons.
B)At a particular gas station, sales decrease with respect to price by 1516 gallons per cent. The rate of change is -1516 gallons per cent. If the price is increased by 10 cents per gallon, the
Change in gas sales is -18,950 gallons. If the price is decreased by 2 cents, gas sales increase by
-3790 gallons.
C)At a particular gas station, sales decrease with respect to price by 1516 gallons per cent. The rate of change is -1516 gallons per cent. If the price is increased by 10 cents per gallon, the
Change in gas sales is -15,160 gallons. If the price is decreased by 2 cents, gas sales increase by
3032 gallons.
D)At a particular gas station, sales decrease with respect to price by 1516 gallons per cent. The rate of change is 1516 gallons per cent. If the price is increased by 10 cents per gallon, the
Change in gas sales is 11,370 gallons. If the price is decreased by 2 cents, gas sales increase by
2274 gallons.

Question 36

Write an equation for the linear function and use it to answer the given question.
The cost of renting a car is a flat $44, plus an additional 0.24 cents per mile that you drive. How far can you drive for $89?

Question 37

The given situation involves a rate of change that you may assume to be constant. Write a statement that describes howone variable varies with respect to another, give the rate of change numerically (with units), and use the rate of changerule to answer the questions.
You drive along the highway at a constant speed of 45 miles per hour. How far do you travel in 3.4 hours? In 6.5 hours? Write a statement that describes how one variable varies with respect to
Another.

A)Your distance traveled changes with respect to time at a rate of 45 miles per hour. The rate of change is 45 mi/hr. In 3.4 hours, you travel 191.25 miles. In 6.5 hours, you travel 365.625
Miles.
B)Your distance traveled changes with respect to time at a rate of 45 miles per hour. The rate of change is 45 mi/hr. In 3.4 hours, you travel 76.5 miles. In 6.5 hours, you travel 146.25 miles.
C)Your distance traveled changes with respect to time at a rate of 45 miles per hour. The rate of change is 45 mi/hr. In 3.4 hours, you travel 153 miles. In 6.5 hours, you travel 292.5 miles.
D)Your distance traveled changes with respect to time at a rate of 45 miles per hour. The rate of change is 45 mi/hr. In 3.4 hours, you travel 114.75 miles. In 6.5 hours, you travel 219.375
Miles.

Question 38

Draw a graph of the function and use the graph to answer the question.
During the month of January, the depth of the snow, at the base of one ski resort, decreased by 2 inches each day. On December 31st there was a base of 64 inches. Graph the equation and use the
Graph to estimate the depth of snow on January 28th.

Question 39

Write an equation for the linear function and use it to answer the given question.
The price of a particular model car is $10,171 today and rises with time at a constant rate of $1146 per year. How much will a new car cost in 4.1 years?

Question 40

Provide an appropriate response.

Question 41

What is comprised of the values of the dependent variable?

A)Range
B)Periodic function
C)Model
D)Domain

Question 42

Solve the equation for the unknown quantity x.

Question 43

True or False? Exponential functions are useful for modeling enviromental issues.

Question 44

Write an equation for the linear function and use it to answer the given question.
In the town of Oak Forest, a 2% local sales tax and a 9% state sales tax are charged on all retail sales. Let p be the before-tax amount of a purchase in dollars. Let T be the after-tax amount of the
Purchase. Find a linear equation that describes how T varies with p. What is the total price of an
Item that costs $50 before taxes?

Question 45

There are currently 67 million cars in a certain country, decreasing by 0.5% annually. How many years will it take for this country to have 38 million cars? Round to the nearest year.

A)673 years
B)29 years
C)113 years
D)58 years

Question 46

Provide an appropriate response.
The population of a town with an initial population of 65,747 grows at a rate of 3.7% per year. Create a table showing the value of the quantity Q for the first 5 years or growth or decay.

Question 47

Solve the equation for the unknown quantity x.

Question 48

What is comprised of the values of the independent variable?

A)Domain
B)Periodic function
C)Range
D)Model

Question 49

Provide an appropriate response.
What is the most compact mathematical representation of a function?

A)Graph
B)Data table
C)Equation
D)Domain

Question 50

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10.

Question 51

Create the required linear function an use it to answer the question.
In 1995 the United States recovered 26% of its municipal solid wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Based on
These two data points, create a linear equation for the function that describes how P varies as a
Function of time.

Question 52

A certain drug is eliminated from the bloodstream exponentially with a half-life of 60 hours. Suppose that a patient receives an initial dose of 10 milligrams of the drug at midnight. Estimate
When the drug concentration will reach 20% of its initial level.

A)139 hours
B)199 hours
C)79 hours
D)23 hours

Question 53

True or False? After 60 years, a population growing at a rate of 4% per year will have grown by
twice as many people as a population growing at a rate of 2% per year.

Question 54

Provide an appropriate response.
Cars sold Crafty Bill's Cool Car Sales opened as a used car sales lot in 2001. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2003?

A)550 cars
B)400 cars
C)500 cars
D)350 cars

Question 55

The population of a town with an initial population of 60,196 is decreasing at a rate of 4.2% per year. Create a table showing the value of the quantity Q for the first 5 years or growth or decay.

Question 56

Write an equation for the linear function and use it to answer the given question.
You can purchase a motorcycle for $7101 or lease it for a down payment of $783 and $243 per month. Find an equation that describes how the cost of the lease depends on time. How long can
You lease the motorcycle before you've paid more than its purchase price.

Question 57

Provide an appropriate response.
The population of a town with an initial population of 64,546 is decreasing at a rate of 3.7% per year. Create an exponential function of the form Q

Question 58

Provide an appropriate response.
The following graph represents a function. Describe the function in words.

A)The function shows a steadily increasing average age of death between 1980 and 2004.
B)The function shows a steadily decreasing average age of death between 1980 and 2004.
C)The function shows that the average age of death increases between 1980 and 1992 and does not change between 1992 and 2004.
D)The function shows that the average age of death per year does not change between 1980 and 2004.

Question 59

Write an equation for the linear function and use it to answer the given question.
Normaltown High School's pool record for the 100-yard freestyle was 47.8 in 1990. Assume that the record falls at a constant rate of 0.03 second per year. What does the model predict for the
Record in 2010?

Question 60

Create the required linear function an use it to answer the question.
Suppose that you were 22 inches long at birth and 3.5 feet tall on your tenth birthday. Based on these two data points, create a linear equation for the function that describes how height varies
With age. Use the equation to predict the height at age 2 and 41.

Question 61

Provide an appropriate response.
The population of a town with an initial population of 70,430 grows at a rate of 2.5% per year. Make a graph of the exponential function.

Question 62

True or False? A linear function has a varying rate of change and a curved graph.

Question 63

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10.

Question 64

Write a short statement that expresses a possible function between the given variables.
(grade of hill, speed of scooter)

A)If you are coasting down a hill on a scooter, the narrower the hill, the faster you will coast.
B)If you are coasting down a hill on a scooter, the steeper the hill, the faster you will coast.
C)If you are coasting down a hill on a scooter, the wider the hill, the slower you will coast.
D)If you are coasting down a hill on a scooter, the steeper the hill, the slower you will coast.

Question 65

Question 66

Solve the equation for the unknown quantity x.

Question 67

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10.

Question 68

Provide an appropriate response.
In the algebraic equation of a line, the y-intercept is denoted by the letter ______.

A)b
B)m
C)y
D)x

Question 69

The given table represents a function. Make a clear graph of the function.

Question 70

Write an equation for the linear function and use it to answer the given question.
You can rent time on computers at the local copy center for a $7 setup charge and an additional $4 for every 5 minutes. How much time can you rent for $16?

Question 71

Solve the equation for the unknown quantity x.

Question 72

Provide an appropriate response.
A toxic radioactive substance with a density of 3 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 34 years ago. If the half-life of the
Substance is 10 years, what was the density of the substance when it was deposited 34 years ago?

A)3.68 mg/cm2
B)0.28 mg/cm2
C)79.17 mg/cm2
D)31.67 mg/cm2

Question 73

Provide an appropriate response.
What is a mathematical representation of a function that provides detailed information but can become unwieldy?

A)Graph
B)Equation
C)Domain
D)Data table

Question 74

Provide an appropriate response.
True or False? The slope is defined as the amount that the graph runs vertically for a given distance that it rises horizontally.

A)False
B)True

Question 75

Provide an appropriate response.
A computer is purchased for $4600. Its value each year is about 76% of the value the preceding year. Find the value of the computer after 8 years.

A)$389.12
B)$27,968.00
C)$295.73
D)$512.00

Question 76

(weight of a bag of candy, price of the bag of candy)

A)As the price of the bag of candy increases, the weight of the bag decreases.
B)As the price of the bag of candy decreases, the weight of the bag increases.
C)As the weight of the bag of candy decreases, the price of the bag increases.
D)As the weight of the bag of candy increases, the price of the bag increases.

Question 77

Write a short statement that expresses a possible function between the given variables.
(number of cars on road, air quality)

A)As the quality of the air deteriorates, the number of cars on the road decreases.
B)As the quality of the air deteriorates, the number of cars on the road increases.
C)As the number of cars on the road decreases, the quality of the air generally deteriorates.
D)As the number of cars on the road increases, the quality of the air generally deteriorates.

Question 78

Solve the equation for the unknown quantity x.

Question 79

True or False? An exponential function grows (or decays)by the same relative amount per unit time.

A)False
B)True

Question 80

Create the required linear function an use it to answer the question.
In 1995 the United States recovered 25% of its municipal wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Based on these
Two data points, create a linear equation for the function that describes how P varies as a function of
Time. Use this function to predict the percentage recycled in 2006.

A)39%
B)44.3%
C)40.7%
D)42.6%