Deck 1: Linear Functions and Change

Question 1

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number r of rabbits (in millions) remaining t months after the release of the virus.
Use a calculator program to find the slope of the regression line for this data. Round to 3 decimal places.

Answer 1

-105.406

Question 2

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number r of rabbits (in millions) remaining t months after the release of the virus.


- Use a calculator program to find the regression line for this data and use this to estimate how many million rabbits were left after 15 months. Round to the nearest whole number.

Answer 2

622

Question 3

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number r of rabbits (in millions) remaining t months after the release of the virus.


- Use a calculator program to find the regression line for this data. What is the physical interpretation of the t-intercept?

A) The decrease in the population if the virus is present an additional month.
B) The number of months the virus took to lower the population by 1 milllion.
C) The initial rabbit population when the virus was introduced.
D) The time in months at which the rabbit population falls to zero.

Answer 3

The time in months at which the rabbit population falls to zero.

Question 4

A study was done that collected data on 100 individuals' grade point averages and the number of hours per week they spent working. A linear regression was done on this data and the corresponding correlation coefficient was 0.3. What does this tell you about the relationship between grade point averages and working?

A) Increasing working does not affect grade point average.
B) Increasing working increases grade point average.
C) Increasing working decreases grade point average.

Question 5

The following figure gives the annual amount of milk produced (in 1000s of pounds) per US milk cow as a function of t, the number of years since 1986. Is the regression line r = 0.34t + 13.4 reasonably correct?

Question 6

The following table shows the cost of a taxi ride, in dollars, as a function of miles traveled.
Estimate

.

Question 7

The following table shows the cost of a taxi ride, in dollars, as a function of miles traveled.
If

, estimate m to 1 decimal place.

Question 8

The following figure shows scatter plots with r values 0.9, 0.5, 0 ,-0.5, and -0.9. Which scatter plot has r value 0.5?

A)
B)
C)
D)
E)

Question 9

The following table gives the number P of people living in a town t years after 1990.


-
Use a calculator program to find the slope of the regression line for this data. Round to 3 decimal places.

Question 10

The following table gives the number P of people living in a town t years after 1990.


-Use a calculator program to find the regression line for this data and use this to estimate how many lived in the year 2011. Round to the nearest whole number.

Question 11

The following table shows the size of a cell phone bill, in dollars, as a function of the number of text messages.


- Use a calculator program to find a regression line for this data. Estimate

using the formula for the regression line.

Question 12

The following table shows the cost of a cell phone bill, in dollars, as a function of the number of texts.
Use a calculator program to find a regression line for this data. From the formula for the regression line, estimate the value of m that satisfies

. Round up to the nearest number of texts.

Question 13

The following table gives the profits (in millions) of a manufacturing company
months after January 1, 2008.


- Use a calculator program to find the vertical intercept of the regression line for this data. Round to 2 decimal places.

Question 14

The following table gives the profits (in millions) of a manufacturing company months after January 1, 2008.


-Use a calculator program to find the regression line for this data and use this to estimate the profit on January 1, 2009. Round your
answer to one decimal place.

Question 15

The following tables give the profits (in millions) of a manufacturing company months after January 1, 2008.
Use a calculator program to find the regression line for this data. What is the physical interpretation of the t-intercept?

Question 16

Does an value of 0.07 seem reasonable for the following set of data?

Question 17

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number r of rabbits (in millions) remaining t months after the release of the virus.
Find the regression line for this data. Round to 3 decimal places.

Question 18

The following table gives the number of people P living in a town t years after 1990. Use a calculator program to find the regression line for this data.

Question 19

The following table shows the cost of a cell phone bill, in dollars, as a function of the number of texts.
Use a calculator program to find a regression line for this data.

Question 20

The following table gives the profits (in millions) of a manufacturing company months after January 1, 2008.
Use a calculator program to find the regression line for this data.

Question 21

Suppose that is linear with an x-intercept of 6 and parallel to . If , then b = _____ and m = _____.

Question 22

Suppose that is linear, passes through the point (-1, 3), and is parallel to . If , then b = _____ and m = _____.

Question 23

Suppose that is linear, has slope -0.5, and forms the hypotenuse of the right triangle lying in Quadrant I whose area is 36 and whose legs lie on the x and y axes. If , then b = _____ and m = _____.

Question 24

The following figure gives lines A, B, C, D, and E. Their equations are given below. Which is the equation for line E ?

A)
B)
C)
D)
E)

Question 25

Mark all of the following functions that are increasing.

A)
B)
C)
D)
E)
F)

Question 26

Mark all of the following functions that have graphs that are parallel.

A)
B)
C)
D)
E)
F)

Question 27

Mark all of the following functions that pass through the point (0, 6).

A)
B)
C)
D)
E)
F)

Question 28

Mark all of the following functions that are neither increasing nor decreasing.

A)
B)
C)
D)
E)
F)

Question 29

Are the lines and parallel, perpendicular, or neither?

Question 30

Many economists believe that a country's inflation rate will rise if its unemployment rate falls. The following figure show the relationship between the inflation rate, I, and the unemployment rate, u, in four different countries.
In which of the four countries does a change in the unemployment rate have no apparent effect on the inflation rate?

Question 31

The following figure show the distance of two horses from the starting point of a race as a function of time. Which horse won the race? (Answer "A" or "B")

Question 32

You need to purchase a new computer printer. The cost of printer A is $80, and its ink cartridges are $29 each. The cost of printer B is $160, and its ink cartridges are $16 each. You estimate that you will need new ink cartridges about once a month. Find equations for the total cost of each printer after t months and use them to determine when you would have invested about the same amount of money in each. Round to the nearest tenth of a month.

Question 33

If and represent the population (in millions) of two countries, A and B, then in what year will the population of country A double the population of country B? Round to 2 decimal places.

Question 34

Find the vertical intercept of the line l shown n the following figure.

Question 35

An airplane has room for 360 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with x coach-fare seats and y first-class seats, with no space wasted. If you found a formula for y as a function of x, what would be the significance of the x-intercept?

A) It is the number of first-class seats that could replace one coach seat.
B) It is the number of coach seats that could replace one first-class seat.
C) It is the number of first-class seats, if there are no coach seats.
D) It is the number of coach seats, if there are no first-class seats.

Question 36

The cost, C, of producing q items is given by the formula , where And m are positive constants. If the quantity produced increases, what happens to the cost of production?

A) It decreases.
B) It stays the same.
C) It increases.
D)

Question 37

At a price of $2.55 per gallon, the average weekly demand by consumers for gasoline is 43 gallons. If the price rises to $2.75, the weekly demand drops to 41 gallons. Assuming demand is linear, let
, where Q is the weekly quantity of gasoline demanded and p is the price per gallon. What is the slope m, along with its economic significance?

A) -0.40; if gasoline prices increase by $1 per gallon, then there will be a 0.40 gallon decrease in weekly demand.
B) -2; if gasoline prices increase by $1 per gallon, then there will be a 2 gallon decrease in weekly demand.
C) -10; if gasoline prices increase by $1 per gallon, then there will be a 10 gallon decrease in weekly demand.
D) -0.20; if gasoline prices increase by $1 per gallon, then there will be a 0.20 gallon decrease in weekly demand.

Question 38

At a price of $3.00 per gallon, the average weekly demand by consumers for gasoline is 40 gallons. If the price rises to $3.05, the weekly demand drops to 35 gallons. Assuming demand is linear, let
, where Q is the weekly quantity of gasoline demanded and p is the price per gallon. What is the economic interpretation of the Q-intercept?

A) The number of gallons demanded if gas were free.
B) The the price at which no gasoline will be demanded.
C) The amount the demand decreases if the price rises $1.
D) The amount the price decreases if the demand is increased by 1 gallon.

Question 39

What is the equation of the line with x-intercept
And y-intercept
?

A)
B)
C)
D)
E) There is not a unique equation for this line.

Question 40

An athlete wanting to strengthen his cardiovascular system will bench-press a weight, w, as many times, N, as possible. The following table shows the relationship between N and w.
Assuming linearity, let N be a function of w. What is the physical interpretation of the slope?

A) The number of bench-presses the athlete can do if there is no weight.
B) The decrease in the number of bench-presses the athlete can do as the weight increases by 1 pound.
C) The decrease in the weight the athlete can lift as an additional bench-press is required.
D) The amount of weight at which the athlete can no longer do any bench-presses.

Question 41

What is the vertical intercept of the line l in the following figure in terms of the constants A and B?

A)
B)
C)
D)

Question 42

The formula for the line intersecting the graph of
at x = 0.1 and x = 0.2 is given by , where b = _____ and m = _____.

Question 43

Find the x-coordinate of the point P shown in the following figure. Round to 3 decimal places.

Question 44

In the following figure, let A = 10 and B = 5. Find the equation of the line through (A, B) and (P, 0) and use it to find the value of P.

Question 45

Suppose that is linear and that and . If , then b = _____ and m = _____.

Question 46

Suppose that is linear with slope -0.5 and passing through the point (-2, 9). If , then b = _____ and m = _____.

Question 47

Suppose that is linear with an x-intercept of -2 and a y-intercept of 4. If , then b = _____ and m = _____.

Question 48

What is the formula for the line graphed in the following figure?

A)
B)
C)
D)

Question 49

If the equation is written in the form , then b = _____ and m = _____.

Question 50

Let define a linear function with slope 1/2 that passes through the point (-1, 6). Then b = _____ and m = _____.

Question 51

Let define a linear function with y-intercept 3 that passes through the point (-1, -1). Then b = _____ and m = _____.

Question 52

Let be the formula for the linear function defined in the following table. Then b = _____ and m = _____.

Question 53

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 55,000 dollars on advertising, it sold 515 cars. Moreover, for each additional 10 thousand dollars spent, they sell 30 more cars. Let be the formula for the number of cars sold as a function of x, the amount of money spent on advertising. Then b = _____ and m = _____.

Question 54

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 55,000 dollars on advertising, it sold 482.5 cars. Moreover, for each additional 10 thousand dollars spent, they sell 15 more cars. Let Be the formula for the number of cars sold as a function of x, the amount of money spent on advertising. What is the practical interpretation of the vertical intercept of the equation?

A) The dollars spent on advertising per car sold.
B) The number of cars sold with no money spent on advertising.
C) The amount of advertising spent before any cars are sold.
D) The number of cars sold per dollar spent on advertising.

Question 55

ComElectric, the Cambridge power company, charges its customers $9.00 a month and $0.068 per kwh, plus a $0.0325 per kwh surcharge. (A kwh, or kilowatt-hour, is a unit of electricity supplied). The formula for the monthly cost for x kwh of electricity is dollars, where b = _____ and m = _____.

Question 56

If a linear population function is 50,000 in year t = 0 and grows by 750 people per year, then , where b = _____ and m = _____

Question 57

At a price of $2.65 per gallon, the average weekly demand by consumers for gasoline is 42 gallons. If the price rises to $2.75, the weekly demand drops to 38 gallons. Assuming demand is linear, let , where Q is the weekly quantity of gasoline demanded and p is the price per gallon. Then b = _____ and m = _____.

Question 58

An airplane has room for 390 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with x coach-fare seats and y first-class seats, with no space wasted. If x = 0, what is the value of y?

Question 59

An airplane has room for 330 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with x coach-fare seats and y first-class seats, with no space wasted. If , then b = _____ and m = _____.

Question 60

If a linear population function is 60,000 in year t = 0 and 90,000 by year t = 20, then , where b = _____ and m = _____.

Question 61

An athlete wanting to strengthen his cardiovascular system will bench-press a weight, w, as many times, N, as possible. The following table shows the relationship between N and w.
Assuming linearity, let . Then b = _____ and m = _____.

Question 62

An athlete wanting to strengthen his cardiovascular system will bench-press a weight, w, as many times, N, as possible. The following table shows the relationship between N and w.
Assuming linearity, what is the maximum weight this athlete will be able bench-press 6 times? Round to the nearest whole number.

Question 63

Find a formula for the linear function that passes through the points (4,-4) and (-3,24)

Question 64

Find a formula for the linear function that passes through the point (3,7) with slope 3.

Question 65

Find a formula for the linear function that has x-intercept -4 and y-intercept 16.

Question 66

The following table shows the relationship between s, the side length of an equilateral triangle, p, the perimeter of the triangle, and A, the area of the triangle.
If A is a linear function of s, give its rate of change. If it is not linear, enter "not linear".

Question 67

A salesman earns , where n is the number of products sold, and is the weekly wage in dollars. What does the number 450 represent? (Mark all that apply)

A) The slope
B) The vertical intercept
C) The salesman's base salary
D) The salesman's commission for each product sold

Question 68

The distance traveled by a car is miles, where t is the number of hours driven. What is the vertical intercept?

Question 69

The distance traveled by a car is Miles, where t is the number of hours driven. What is the meaning of the number 80? (Mark all that apply)

A) The vertical intercept
B) The slope
C) The total distance traveled
D) The speed of the car

Question 70

Could the following table represent a linear function?

Question 71

Could the following table represent a linear function?

Question 72

Could the following table represent a linear function?

Question 73

Which of the following figures shows the graph of a person's weight, w, as a function of time t, in months if the person starts out at 150 pounds and loses 10 pounds a month?

A)
B)
C)
D)

Question 74

One of the functions represented in the table below is linear. What is its vertical intercept?

Question 75

For the line ,
a) what is the slope of the line?
b) what is the y-intercept of the line?

Question 76

A cookie store has a fixed monthly cost of $550. It costs the cookie store $0.25 to make a cookie and the store sells each cookie for $1.50. Express revenue R, cost C, and profit P for the cookie store when making and selling cookies in a month.

Question 77

A certain baseball card's value is given by
where is the number of years after the card was issued. Interpret the constants 1.1 and 4.2.

Question 78

The population of a pack of rats can be represented by the formulaWhere Represents the population in hundreds, and represents the time, in months, since January 2010. Which of the following is correct regarding the vertical intercept?

A)
B)
C)
D)

Question 79

The population of a pack of rats can be represented by the formulaWhere Represents the population in hundreds, and Represents the time, in months, since January 2010. Which of the following is correct regarding the slope.

A)
B)
C)
D)

Question 80

A wildlife ranger finds that there is a linear relationship between the number of bushels of corn distributed in a month and the number of deer at the park. If the ranger distributes no bushels of corn, there are 47 deer at the park. For each additional bushel of corn distributed, 7 more deer come to the park.
a) If ^d is the number of deer at the park and ^b is the number of bushels of corn fed in a month, find a formula for ^d in terms of ^b .
b) How many deer are at the park if the ranger feeds 2 bushels of corn?
c) How many bushels of corn must be distributed in order to have ⁷⁵ deer at the park?