Resources

Resources

Interpreting Linear Expressions

The original selling price of a share of stock was

d

dollars. The selling price for a share of the same stock at a later date was represented by the expression

1.5(0.05 d)

. Which description could explain what happened to the price of the share of stock?

\newline

The price decreased by

95 \%

and then increased by

50 \%

\newline

The price decreased by

0.95 \%

and then increased by

150 \%

\newline

The price increased by

0.5 \%

and then decreased by

5 \%

\newline

The price increased by

50 \%

and then decreased by

0.95 \%

1.07(0.55 p)

represents the total amount Eli paid for a jacket originally priced

p

dollars. Which changes to the original price could have resulted in this expression?

\newline

0.07 \%

and then a discount of

55 \%

\newline

45 \%

7 \%

\newline

0.45 \%

0.07 \%

\newline

45 \%

0.07 \%

Xin invests money in an account paying a simple interest of

3.5 \%

m

represents the amount of money she invests, which expression represents her balance after a year, assuming she makes no additional withdrawals or deposits?

\newline

1+0.035

\newline

3.5 m

\newline

m+0.035 m

\newline

m+0.035

The original selling price of a share of stock was

d

dollars. The selling price for a share of the same stock at a later date was represented by the expression

1.4(0.55 d)

. Which description could explain what happened to the price of the share of stock?

\newline

The price decreased by

55 \%

and then increased by

140 \%

\newline

The price increased by

40 \%

and then decreased by

45 \%

\newline

The price decreased by

0.45 \%

and then increased by

140 \%

\newline

The price decreased by

0.55 \%

and then increased by

0.4 \%

The original selling price of a share of stock was

d

dollars. The selling price for a share of the same stock at a later date was represented by the expression

0.2(1.15 d)

. Which description could explain what happened to the price of the share of stock?

\newline

The price increased by

15 \%

and then decreased by

0.2 \%

\newline

The price increased by

115 \%

and then decreased by

20 \%

\newline

The price decreased by

20 \%

and then increased by

0.15 \%

\newline

The price increased by

15 \%

and then decreased by

80 \%

The original selling price of a share of stock was

d

dollars. The selling price for a share of the same stock at a later date was represented by the expression

0.2(1.65 d)

. Which description could explain what happened to the price of the share of stock?

\newline

The price increased by

165 \%

and then decreased by

0.8 \%

\newline

The price increased by

65 \%

and then decreased by

80 \%

\newline

The price decreased by

0.2 \%

and then increased by

65 \%

\newline

The price decreased by

80 \%

and then increased by

165 \%

D=1,874-0.55 t

\newline

D

, in meters, between an antarctic glacier and the coast

t

days after January

1

2010

is approximated by the equation. How does the distance between the glacier and the coast change over time?

\newline

1

\newline

(A) The glacier moves

0

55

meters per day closer to the shore.

\newline

(B) The glacier moves

1

874

meters per day closer to the shore.

\newline

(C) The glacier moves

0

55

meters per day further from the shore.

\newline

(D) The glacier moves

1

874

meters per day further from the shore.

D

in millions of miles of the voyager

1

space craft from the sun

m

months after January

1

2015

is approximately by the equation

D=27.4m+12,100

. What is the best interpretation of

27.4

as shown in the given equation?

A once-popular children's doll is slowly declining in popularity. The quartic function

\newline

f(x)=0.002 x^{4}+0.025 x^{3}-0.364 x^{2}-7.243 x+86.993

\newline

x

is the number of years since

1993

, can be used to estimate the number of dolls of this type that were sold (in thousands) during a given year from

1993

2003

. Estimate how many dolls were sold in

1997

h=16,890-3.4t

\newline

h

, in feet, of a mountain at a time,

t

, measured in thousands of years from the present is given by the equation. What is the best interpretation of

16,890

as shown in the given equation?

\newline

1

\newline

(A) The height of the mountain is presently

16,890

\newline

(B) The height of the mountain will reach

0

16,890

years from now.

\newline

(C) The height of the mountain increases by

16,890

feet every thousand years.

\newline

(D) The height of the mountain decreases by

16,890

feet every thousand years.

5^{1.15^x}

gives the area, in square meters, of forest damaged by a fire as a function of minutes since the fire was discovered. How many square meters of forest was damaged when the fire was discovered?

Fiona's Fashion Store is world renowned for its buttoned uniforms.

\newline

A collection of

36

42

jackets contains

842

buttons. A collection of

6

7

jackets contains

137

buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons.

\newline

How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?

\newline

1

\newline

(A) There is not enough information to determine the exact number of buttons in a shirt or jacket.

\newline

(B) The given information describes an impossible situation.

\newline

10

buttons in a single shirt and

11

buttons in a single jacket.

\newline

11

buttons in a single shirt and

10

buttons in a single jacket.

A sequence starts at

10

. The term-to-term rule is to subtract

3

then multiply by

2

\newline

a) Work out the fourth term of the sequence.

\newline

b) Is this sequence increasing, decreasing or neither?

A research probe needs to be

0.5

meters under the ground. It is known that the probe must be traveling

140

meters per second at impact to reach a depth of

0.5

meters. If the probe is dropped from

10b^2

(b is constant) meters above the ground and the distance traveled is given by the function

s(t) = 4.9t^2

. Find the value of

b

and the height the probe should be dropped from.

Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after

1.5

hours of driving, her altitude was

710

meters above sea level. Her altitude increased at a constant rate of

740

meters per hour.

\newline

y

represent Noa's altitude (in meters) relative to sea level after

x

\newline

Complete the equation for the relationship between the altitude and number of hours.

P(t)=1,800(1.004)^{t}

\newline

The function models

P

, the amount of money, in dollars, in Yara's savings account

t

years after she opened the account with an initial deposit of

\$ 1,800

. How much money is in Yara's account

5

years after her initial deposit if she makes no deposits or withdraws in that time?

Kiran has a collection of vintage action figures that is worth

\$ 320

. If the collection appreciates at a rate of

14.8 \%

per year, which equation represents the value of the collection after

8

\newline

V=320(1+0.148)

\newline

V=320(1.148)^{8}

\newline

V=320(0.148)^{8}

\newline

V=320(1-0.148)^{8}

A town has a population of

118

600

and grows at a rate of

5 \%

every year. Which equation represents the town's population after

4

\newline

P=118,600(1+0.05)^{4}

\newline

P=118,600(1+0.05)

\newline

P=118,600(0.05)^{4}

\newline

P=118,600(0.95)^{4}

In a lab experiment, a population of

500

bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after

4

\newline

B=500(1+3)^{4}

\newline

B=3(500)^{4}

\newline

B=3(1+500)^{4}

\newline

B=500(3)(3)(3)(3)

A town has a population of

27

000

and shrinks at a rate of

8 \%

every year. Which equation represents the town's population after

7

\newline

P=27,000(0.2)^{7}

\newline

P=27,000(0.92)^{7}

\newline

P=27,000(1-0.08)(1-0.08)(1-0.08)

\newline

P=27,000(0.08)^{7}

P = 23 + 10(h - 1)

People start waiting in line for the release of the newest cell phone at

5

a.m. The equation gives the number of people,

P

, in line between the hours,

h

6

11

a.m., when the doors open. Assume that

6

a.m. is when time

h = 1

. What does the

23

mean in the equation?

5.5 B+4R=28

The given equation models the cost if Amit picks

B

pounds of blueberries and

R

pounds of raspberries at a farm where blueberries cost

\$5.50

per pound and raspberries cost

\$4.00

per pound. According to the equation, how much does Amit spend in total on both types of berries? Choose

1

(A) \$\$9.50

\$22.00

\$28.00

\$56.00

Lauren launches a toy rocket from a platform. The height of the rocket in feet is given by

h(t)=-16 t^{2}+48 t+28

t

represents the time in seconds after launch. What is the appropriate domain for this situation?

\newline

For the function

f

f(0) = 86

, and for each increase in

x

1

f(x)

80\%

. What is the value of

f(2)

Water leaking onto a floor forms a circular pool. The area of the pool increases at a rate of

16\,\text{picm}^{2}/\text{min}

. How fast is the radius of the pool increasing when the radius is

7\,\text{cm}

A perfect cube shaped ice cube melts so that the length of its sides are decreasing at a rate of

2\frac{\text{in}}{\text{sec}}

. Assume that the block retains its cube shape as it melts. At what rate is the volume of the ice cube changing when the sides are

7\text{in}

Chase signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded. His total cost per month is given by the equation

c=7.99+1.25 x

x

represents the number of songs he downloads and

c

represents the total cost, in dollars and cents. What could the number

7

99

represent in the equation?

\newline

The total cost per month assuming one song is downloaded.

\newline

The cost to download

100

\newline

The change in the total cost for every one additional download.

\newline

The base cost of the streaming service per month.

Nakeisha is driving on a long road trip. She wrote an equation to represent how many gallons of gas she has left in her tank,

g=11-0.45 h

g

represents the number of gallons and

h

represents time in hours. What is the meaning of the

g

h=1

\newline

The number of gallons of gas initially in the tank.

\newline

The change in the number of gallons of gas in the tank for every one additional hour.

\newline

The number of gallons in the tank after one hour.

\newline

The number of gallons in the tank when the trip ends.

At the beginning of spring, Lily planted a small sunflower in her backyard. The sunflower's height in inches,

h

w

weeks, is given by the equation

h=4 w+18

. What could the number

4

represent in the equation?

\newline

The sunflower's height after one week.

\newline

The rate of change in the sunflower's height.

\newline

The sunflower's final height

\newline

The sunflower's height when it was planted.

Jose's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation

y=67+6.6 x

y

represents the expected quiz score and

x

represents hours spent on homework that week. What is the meaning of the

y

x=1

\newline

A student's expected quiz score if they spent

73

6

hours on their homework.

\newline

The change in expected quiz score for every additional one hour students spend on their homework.

\newline

A student's expected quiz score if they spent

1

hour on their homework.

\newline

A student's expected quiz score if they spent no time on their homework.

At the beginning of spring, Anand planted a small sunflower in his backyard. The sunflower's height in inches,

h

w

weeks, is given by the equation

h=3.75 w+18

. What could the number

3

75

represent in the equation?

\newline

The rate of change in the sunflower's height.

\newline

The sunflower's final height

\newline

The sunflower's height after one week.

\newline

The sunflower's height when it was planted.

Ajay is preheating his oven before using it to bake. Ajay wants to predict the final temperature after

x

minutes. He wrote the equation

y=45 x+79

y

represents the final temperature in degrees Fahrenheit. What is the meaning of the

y

x=1

\newline

The oven's temperature after

1

\newline

The change in minutes for every change of one degree Fahrenheit.

\newline

The rate of change in the oven's temperature over time.

\newline

The time when the oven's temperature is

0^{\circ}

Melissa and Rachel like to make funny hats. Melissa has made

20

zebra-printed hats, and Rachel has made

h

striped hats. Together they have made a total of

42

\newline

Write an equation to describe this situation.

\newline

1350(1.05)^t

models the average wages, in dollars, in the US as a function of the number of years since

1930

\newline

1.05

represent in this expression?

\newline

1

\newline

(A) The average wages double every

1.05

\newline

(B) The average wages in the US were about

\newline

\$1.05

1930

\newline

(C) The average wages in the US increase by about

\newline

5\%

The amount in moles,

m

, of a reactant

s

seconds after the start of a chemical reaction is given by the equation

m= 0.15(8.6-s)

. Which of the following is the best interpretation of the number

0.15

\newline

(A) The initial amount of reactant was

0.15

\newline

(B) The amount of reactant decreases by

0.15

moles per second.

\newline

(C) No reactant remains

0.15

seconds after the start of the chemical reaction.

\newline

(D) The amount of reactant begins to decrease

0.15

seconds after the start of the chemical reaction.

Jack's mother gave him

50

chocolates to give to his friends at his birthday party. He gave

3

chocolates to each of his friends and still had

2

chocolates left. If

x

is the number of friends at Jack's party, which of the following equations best describes the situation?

The rate of change

\frac{d P}{d t}

of the number of algae in a tank is modeled by a logistic differential equation. The maximum capacity of the tank is

630

1 \mathrm{PM}

, the number of algae in the tank is

227

and is increasing at a rate of

39

algae per minute. Write a differential equation to describe the situation.

\newline

\frac{d P}{d t}=\square

The rate of change

\frac{d P}{d t}

of the number of people on an island is modeled by a logistic differential equation. The maximum capacity of the island is

926

11 \mathrm{AM}

, the number of people on the island is

135

and is increasing at a rate of

28

people per hour. Write a differential equation to describe the situation.

\newline

\frac{d P}{d t}=\square \text { Submit Answer }

The rate of change

\frac{d P}{d t}

of the number of students who heard a rumor is modeled by a logistic differential equation. The maximum capacity of the school is

720

3 \mathrm{PM}

, the number of students who heard the rumor is

115

and is increasing at a rate of

47

students per hour. Write a differential equation to describe the situation.

\newline

\frac{d P}{d t}=\square \text { Submit Answer }

The rate of change

\frac{d P}{d t}

of the number of people entering a movie theatre is modeled by a logistic differential equation. The maximum capacity of the theatre is

775

12 \mathrm{AM}

, the number of people at the movie theatre is

246

and is increasing at a rate of

36

people per hour. Write a differential equation to describe the situation.

\newline

\frac{d P}{d t}=\square \text { Submit Answer }

A school charges

\$6

per ticket to a dance. They spend

\$300

on music and decorations. The expression

6n-300

describes the amount of profit the school makes from the dance if

n

students buy tickets. What does

6n

represent in this context?

\newline

1

\newline

(A) The amount of money the school charges for all

n

\newline

(B) The amount of money the school spends on the dance

\newline

(C) The number of students who buy tickets

\newline

(D) The profit the school earns per ticket

A lake near the Arctic Circle is covered by sheet of ice during the cold winter months. When spring arrives, the ice starts to melt.

\newline

S

models the ice sheet's thickness (in meters) after

t

\newline

S = -0.25t + 4

\newline

What is the ice sheet's thickness at the beginning of spring?

M=8(4.5-C)

\newline

The magnetic field,

M

, in microtesla, at the center of a loop with a current of

C

milliamps clockwise is given by the equation. By how many microteslas does the magnetic field change for a

1

milliamp increase in the current?

\newline

1

\newline

-8

\newline

-4.5

\newline

28

\newline

36

E_{s}=6.11 \cdot 10^{\frac{7.5 T}{237.3+T}}

\newline

The saturation vapor pressure over water,

E_{s}

, measured in hectopascals, is the vapor pressure of the air when the number of water molecules condensing equals the number evaporating from a flat surface of water. The equation shown models the relationship between

E_{s}

and the temperature,

T

, in degrees Celsius, of the air and water. Which of the following best describes the meaning of

6

11

in this context?

\newline

1

\newline

(A) This is the saturation vapor pressure when the temperature is

0

degrees Celsius.

\newline

(B) This is the saturation vapor pressure when the temperature is

1

degree Celsius.

\newline

(C) This is the saturation vapor pressure when the temperature is

10

degrees Celsius.

\newline

(D) This is the saturation vapor pressure when the temperature is

100

degrees Celsius.

D=32(1.16)^{\frac{q}{4}}

\newline

The given equation models the total number of downloads in thousands,

D

, of a mobile game

q

quarter years after it officially launches. Based on the model, which of the following statements is true?

\newline

1

\newline

(A) The number of total downloads increases by

16 \%

\newline

(B) The number of total downloads increases by

64 \%

\newline

(C) The number of total downloads increases by

16 \%

each quarter year.

\newline

(D) The number of total downloads increases by

64 \%

each quarter year.

The rate of change

\frac{d P}{d t}

of the number of yeast in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{3768}{20227} P\left(1-\frac{P}{942}\right)

\newline

t=0

, the number of yeast in the tank is

226

and is increasing at a rate of

32

yeast per minute. What is the limiting value for the total number of yeast in the tank as time increases?

\newline

The rate of change

\frac{d P}{d t}

of the number of students who heard a rumor is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{379}{4760} P\left(1-\frac{P}{758}\right)

\newline

t=0

, the number of students who heard the rumor is

238

and is increasing at a rate of

13

students per hour. At what value of

P

P(t)

growing the fastest?

\newline

The rate of change

\frac{d P}{d t}

of the number of people at a carnival is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{515}{8584} P\left(1-\frac{P}{824}\right)

\newline

t=0

, the number of people at the carnival is

232

and is increasing at a rate of

10

people per hour. What is the limiting value for the total number of people at the carnival as time increases?

\newline

The rate of change

\frac{d P}{d t}

of the number of deer on an island is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{4}{8721} P(754-P)

\newline

t=0

, the number of deer on the island is

108

and is increasing at a rate of

32

deer per day. Find

\lim _{t \rightarrow \infty} P^{\prime}(t)

\newline

The rate of change

\frac{d P}{d t}

of the number of bears at a national park is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{7280}{71839} P\left(1-\frac{P}{560}\right)

\newline

t=0

, the number of bears at the national park is

199

and is increasing at a rate of

13

bears per day. Find

\lim _{t \rightarrow \infty} P^{\prime}(t)

\newline