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A.CED.2 [576454]StudentClassDate

Read the following and answer the questions below:

Going to a Baseball Game

Going to a Baseball GameChris is a big fan of the baseball team in the city where she lives, and she loves to go to the games with her family. Chris and her dad are planning a trip to a game for four people. He asked her to determine how much it will cost for their tickets and snacks at the game. Chris’s dad thinks they may go to several games this year.They chose the section of the park where they wanted to sit, and Chris found the prices for seats in that section. She found three ways to buy the tickets.

Individual game tickets for the section they chose are $30 per ticket. The cost of a 21-game package of tickets for one seat in their section is

$20 per game. A package of 10 tickets costs $200, and they can be used in any

combination of single tickets per game or multiple tickets per game in their section.

Chris thinks they will each want a hot dog and a soft drink, and two people can share a bag of peanuts. This table shows the cost of those items at the game.

FOOD COSTSFood Item CostHot dog $6.00Soft drink $4.50Peanuts $5.00

An additional cost will be the $20 charge at the parking lot.

1. Read "Going to a Baseball Game" and answer the question.

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The people who attended the second game purchased h hot dogs, d soft drinks, and 2 bags of peanuts. They spent a total of $61 on food.Which equation represents the cost spent on food?

A.

B.

C.

D.

Read the following and answer the questions below:

Pollution Research

Pollution ResearchIn her environmental science class, Kaylie has been learning about air pollution. The teacher told the class that pollution occurs when chemicals and particles are released into the air we breathe. These pollutants can be very harmful to people and other living organisms in the environment.Several natural processes release pollutants. Most pollution is caused by human activities that release hazardous chemicals into the air through their exhaust: when cars run and burn gasoline, when factories use coal for fuel, or even when gas stoves are used to cook food. These chemicals, when exposed to sunlight, can react with other substances to form smog, which is the haze that is often seen surrounding large cities. Air pollution and smog are harmful to people’s health and to the environment. They have been known to aggravate asthma and respiratory disease as well as to cause acid rain.

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Kaylie is interested in learning more about what causes air pollution and what she can do to minimize it. She has noticed that the city she lives in has areas with more smog than others. She would like to know what chemicals are present in the air in this city. She goes to the local climate research center to get more information.At the research center, scientists inform Kaylie that the main source of pollution in the area is car exhaust from commuters traveling in and out of the city every day. Car exhaust produces a chemical known as nitrogen dioxide that can absorb light and eventually create pollutants. The scientists tell Kaylie that when nitrogen dioxide breaks down, it forms particles of oxygen that are different from the oxygen we breathe. These oxygen particles combine with other substances in the air to form pollutants. Kaylie realizes that when the nitrogen dioxide from car exhaust breaks down and decreases in amount, this means that oxygen particles, and therefore pollutants, are being formed and are increasing in amount.The scientists at the research center have been doing pollution experiments in their laboratories. They have been comparing the amount of nitrogen dioxide that breaks down with the amount of oxygen particles formed. They do this by measuring the concentrations of these substances over short periods to see how they change. Concentrations are determined by finding the amount of a substance per unit volume. In this case, the scientists measured concentration in micrograms per cubic meter They let Kaylie look at the results from a recent investigation.

These results show how the concentration of nitrogen dioxide and oxygen particles changed in relation to one another over a period of 20 minutes. After looking at the results, Kaylie is convinced that nitrogen dioxide is

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harmful to the environment. She will remember her trip to the research center the next time she needs to go somewhere. Maybe she will try walking or riding her bike more often!

* Micrograms are very small units that are a fraction of a gram, so

2. Read "Pollution Research" and answer the question.Kaylie’s classmates do a pollution experiment in which they measure growth of the same type of plant over the course of three weeks in two different areas. Area 1 has a high concentration of nitrogen dioxide. Area 2 has a low concentration of nitrogen dioxide. They compile their results in the tables below.

If x represents the time (in weeks) and y represents the plant height (in centimeters), which equations represent the growth of the plants in the different areas?

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A. Area 1:

Area 2:

B. Area 1:

Area 2:

C. Area 1:

Area 2:

D. Area 1:

Area 2:

3. The width of a rectangle is 3 more than its length. The dimensions of a second rectangle are 25% of the dimensions of the first rectangle. Which equation can be used to determine the area of the second rectangle, A, in terms of the length, l, of the first rectangle?

A. A = 0.0625l2 + 0.1875l

B. A = 0.25l2 + 0.75l

C. A = 0.5l2 + 1.5l

D. A = l2 + 3l

4. A business buys a computer for $3,000. After 4 years, the value of

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the computer is expected to be $250. The value, V, can be related to the time in years, t, in a linear equation. Which equation models the relationship between V and t?

A. V = 250t

B. V = 12t

C. V = 687.50t – 3,000

D. V = –687.50t + 3,000

5. A box manufacturing company compared the volume of several rectangular boxes with the same lengths and widths but varying heights as shown in the table.

Which equation can be used to find the volume, v, for one of these boxes with a height of h?

A.

B.

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C.

D.

6. Adam purchased a baseball card for $0.75.

The value of the card at the time he purchased it was 5% less than the price he paid for the card.

The value of the card has increased by $0.83 every year since he purchased the card.

Which equation models the value, v, of the card tyears after Adam purchased the card?

A. v = 0.83t + 0.71

B. v = 0.83t + 0.75

C. v = 0.75t + 0.83

D. v = 0.71t + 0.83

7.Which graph represents the function

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A.

B.

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C.

D.

8. Grace opens a lemonade stand in her neighborhood to earn money. For each cup of lemonade she sells, Grace earns $0.50 profit. Considering that it cost her $6 in start-up costs, Grace graphed her potential profits below, where x represents the number of cups of lemonade she sells and y represents the amount of profit earned in dollars.

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However, Grace made a mistake with her graph. Her y-intercept was incorrectly drawn. At what value should the graph have crossed the y-axis?

9. Thomas rented a van for $65 a day, plus $0.35 for each mile he drove over 3,000 miles. Thomas rented the van for 8 days and drove it m miles. Which equation models the total cost, C, that Thomas paid to rent the van if m ≥ 3,000?

A. C = 520 + 0.35(m – 3,000)

B. C = 520 + 0.35(m + 3,000)

C. C = 65 + 35(m – 3,000)

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D. C = 65 + 0.35m

10. Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?

A. V = 1,000 + 5t

B. V = 1,000 + 1.05t

C. V = 1,000(0.05)t

D. V = 1,000(1.05)t

11. The cost of a notebook, x, is twice the cost of a pen, y. Which equation can be used to represent this relationship?

A.

B.

C.

D.

12. Mary is performing an experiment in a chemistry lab. She made T liters of a 20% acid solution using x liters of 12% acid solution A and y liters of 30% acid solution B. Which equation shows the correct relationship between x, y, and T?

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A.

B.

C.

D.

13. Suppose a forest starts with a deer population of 35 deer. The population is increasing at a rate of 12% per year. Which equation represents the population of deer after x years?

A. y = 12(0.35)x

B. y = 12(1.35)x

C. y = 35(0.12)x

D. y = 35(1.12)x

14. Sunnydale had a population of 3,250 people in the year 2000. The population has been increasing by 2.5% every year after 2000. Which equation models the population, P, based on the number of years after 2000, t?

A. P = 3,250(1.025)t – 2000

B. P = 3,250(2.5)t – 2000

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C. P = 3,250(1.025)t

D. P = 3,250(2.5)t

15. A rabbit weighed 4 ounces when it was born. The rabbit gained 2 ounces each week for the next 12 weeks. Which equation models the weight of the rabbit, w, x weeks after it was born, where x ≤ 12?

A. w = 6x

B. w = 2x – 4

C. w = 2x + 4

D. w = 4x + 2

16. Theo kept track of the time and distance traveled while walking and riding his bike from home. His results are shown in the line graphs.

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Which pair of equations best represents the time t and distance d relationships in the graphs?

A.

B.

C.

D.

17. A unit conversion table shows the number of x liters in y gallons.

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Which equation can be used to represent this relationship?

A.

B.

C.

D.

18. A farmer has a farm that is T acres on which he plants two different crops, crop A and crop B. For each acre of crop A planted, the farmer's expenses are $20 less than the expenses for each acre of crop B, which are z dollars. If the farmer plants x acres of crop A and y acres of crop B, which equation represents the total expenses, C, for planting both crops?

A.

B.

C.

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D.

19. Mikel has $20 to spend at the aquarium.

The aquarium charges a $10 admission fee. The aquarium also has special exhibits that cost $4.00 each to

view.

Which equation can be used to determine the amount of money, y, that Mikel has left if he views xexhibits?

A. y = 4 – 10x

B. y = 10x – 4

C. y = 10 – 4x

D. y = 4x – 10

20. Mrs. Baker charges an initial fee of $20 to clean a house. She charges an additional $5 for each hour it takes her to clean the house. Which graph shows the total cost, y, that Mrs. Baker charges if she spends x hours cleaning a house?

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A.

B.

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C.

D.

21. The function is a linear function of x:

. for all x and for all constant bAs well, f(x, y) is a linear function of y:

for all y and for all constant a.

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The following values are known:

What is

A. 9

B. 42

C. 54

D. 66

22. Stan correctly graphed the equation on grid paper. Which group of ordered pairs and explanation are true about the graph of this equation?

A. a curve through the points

B. a line through the points

C. a curve through the points

D. a line through the points

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23. Jeremiah drank three 8-oz cups of coffee. Each cup of coffee contained 130 mg of caffeine. Jeremiah’s body eliminates 13% of the caffeine each hour. Which equation represents the amount of caffeine, C, in his body after t hours?

A. C = 130(0.13)t

B. C = 390(0.13)t

C. C = 130(0.87)t

D. C = 390(0.87)t

24. The owner of a local coffee shop is designing a sign board to display the coffee specials. She decides to make the height of the board one-third its width, x. The printing cost of the board depends upon its area, For this reason, the owner tries different sizes for the board and records the areas. Use the coordinate plane below to graph the relationship between the two quantities when the domain is

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25. Of the 17,000 students that attend City College, 30% are freshmen. As the semester progresses 5 freshmen per week transfer to other universities. Which equation models the number of freshmen, f, at City College t weeks into the semester?

A.

B.

C.

D.

26. Nicole and her sister each invest $500 in a bank account that earns an annual interest rate of 4%. If y represents the total amount of money in the account and t represents the time in years since they invested in the account, which equation represents this situation?

A.

B.

C.

D.

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27. Mary has written 10 pages for her novel. She plans to write 15 additional pages per month until she is finished. Which equation represents the total number of pages Mary has written, p, after m months?

A. p = 10m + 15

B. p = 10m – 15

C. p = 15m + 10

D. p = 15m – 10

28. The label on a bottle of juice shows that it has N calories. A bottle of the juice contains M grams of sugar, and each gram of sugar has K calories. If the juice is a mixture of sugar and some other ingredients, write an equation that shows what percentage, P, of the total calories in the bottle represents the calories that come from the sugar in the juice.

29. A certain population of bacteria doubles in number every two hours. A scientist starts with 1,000 bacteria. The graph models the growth of the bacteria over time.

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Write an equation that models the relationship between t, the time in hours, and b, the number of bacteria.

30. When Brendan kicks a football, its height in feet can be modeled by the equation where t is the time, in seconds, after Brendan kicks the ball. What is the value of t when the football reaches its maximum height, rounded to the nearest tenth?

A. 0

B. 2.3

C. 2.7

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D. 5.3

31. Two planes are flying on straight paths toward each other and are D horizontal miles apart. The speed of one plane is 220 mph, and it passes the other plane after 4 hours. How is the distance, D (in miles), between the planes related to the speed, x (in mph), of the other plane?

A.

B.

C.

D.

32. There were 36 students absent from a school on Tuesday.

3% of the boys were absent. 7% of the girls were absent.

Which equation models the total number of boys, x, at the school in terms of the total number of girls, y, at the school?

A.

B.

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C.

D.

33. A cell phone plan costs $49 per month for 200 minutes. For each minute over 200, the customer is charged an additional $0.10 per minute. Which equation could be used to calculate the monthly bill, y, if a person talked x minutes over 200 in a month?

A. y = 0.1x + 49

B. y = 0.1x + 249

C. y = 0.1(200 – x) + 49

D. y = 0.1(x – 200) + 49

34. Mr. Frank bought a car that cost $33,000 dollars. The car depreciates approximately 12% of its value each year. Which equation represents the value, v, of the car after t years?

A. t = 33,000(0.12)v

B. v = 33,000(0.12)t

C. t = 33,000(0.88)v

D. v = 33,000(0.88)t

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35. Jane invested $755 in an account that earns interest at a rate of 8.5%, compounded annually. Which equation can be used to determine the value, v (in dollars), of Jane’s investment after t years?

A. v = 755 + 1.085t

B. v = 755(1.085t)

C. v = 755(1.085)t

D. v = [755(1.850)]t

36. The period (T) of a mass attached to a spring is equivalent to the product of and the square root of the ratio of the mass (m) to the spring constant (k). Which equation represents this relationship?

A.

B.

C.

D.

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37. Ana orders several yards of fabric online. Each yard costs $3, and the company charges $4 to ship each order.A graph of the equation that models the cost, y, of ordering x yards of fabric is shown below:

Which equation determines the cost of ordering x yards of fabric?

A.

B.

C.

D.

38. Leah, Michelle, and Bruce are using tiles to create different arrangements. Each of them is given a turn to make a change in their arrangement and establish a pattern.

Leah starts with 1 tile. On her second turn, she adds 1 tile to the length and 1 tile to the width to make a square. She then keeps adding enough tiles to keep making a square on each turn, as shown below.

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Michelle starts with 3 tiles. She adds 2 tiles on the second turn and continues this pattern, as shown below.

Bruce starts with 1 tile. He doubles the number of tiles on each turn.

Part A. Write an equation to represent each of the three students’ patterns. Let t represent the number of tiles and x represent the turn number.

Part B. On the same set of axes, graph and label the equations you wrote in part A.

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Part C. During which turns will Bruce have the most tiles? During which turns will Michelle have the most tiles? During which turns will Leah have the most tiles? Explain how you can see this on your graph.

Part D. Create an equation that models a tile pattern that will always have more tiles than any of the other players have. What rules would you use for creating such a pattern?

Use words, numbers, and/or pictures to show your work.

39. A colony of bacteria grows at a rate of 8% every 2 hours. The colony began with 100 bacteria. Which equation can be used to determine the number of bacteria, B, in the colony after t hours?

A.

B.

C.

D.

40. Amy invested $3,200 at an annual interest rate of 8%. Which

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equation models the value of the investment, V, after t years?

A. V = 3,200(0.08)t

B. V = 3,200(0.8)t

C. V = 3,200(1.08)t

D. V = 3,200(1.8)t

41. Andrew purchased a car for $19,500. The value of the car depreciates at a rate of 8.6% each year. Which equation models the value of Andrew’s car, y, after x years?

A. y = 19,500(1.914)x

B. y = 19,500(1.086)x

C. y = 19,500(0.914)x

D. y = 19,500(0.086)x

42. Sarah earned $1,500 this summer. She mowed lawns for $15 per lawn and babysat for $20 per hour. Which equation represents her earnings from mowing x lawns and babysitting y hours?

A. 1,500 = xy(15 + 20)

B. 1,500 = 5(x + y)

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C. 1,500 = 15x + 20y

D. 1,500 = 35(x + y)

43. A chemist made 50 ounces of an acidic solution by mixing two different concentrations of the solution. He mixed x ounces of acidic solution with an 80% concentration and an acidic solution with a 90% concentration. Which equation can be used to determine the concentration of the final solution?

A.

B.

C.

D.

44. The value of a computer has decreased by 23% each year since it was purchased. The computer was valued at $1,500 when it was purchased. Which equation models the value of the computer, V, t years after it was purchased?

A. V = 0.77(1,500)t

B. V = 1.23(1,500)t

C. V = 1,500(0.77)t

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D. V = 1,500(1.23)t

45. Melissa put $500 into a savings account and had a $525 balance in the account one year later. Melissa does not make any deposits or withdrawals into this account and the account continues to increase exponentially in the same way. Which equation can be used to find y, the balance in the account in dollars in x years?

A.

B.

C.

D.

46. The population of a town is growing by 2% every 3 years. There were 1,000 people living in the town in 1990. Which equation models the population of the town, p, t years after 1990?

A.

B.

C.

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D.

47. A phone company charges a $45 monthly fee for 500 minutes of phone use. For each minute over 500, the phone company charges an additional $0.08. Which equation can be used to determine the total amount the company charges, t, for a phone call that is m minutes long, where m is greater than 500?

A. t = 0.08m + 45

B. t = 45 – 0.08(m – 500)

C. t = 0.08(m – 500) + 45

D. t = 0.08(m + 500) + 45

48. A student has a piece of string 50 inches in length.

He cuts the string in half so that each new piece of string is 25 inches long. Then he cuts each 25-inch piece in half, so that each new piece of string is 12.5 inches

long. Then he cuts each 12.5-inch piece in half and determines the length of each new piece of

string.

Which equation can be used to determine y, the length of each new piece of string in inches after x cycles of cutting each piece in half?

A.

B.

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C.

D.

49. The population in a city was 13,400 in 2010. Research indicates that the population is growing at a rate of 4.5% each year. Which equation models the population, p, of the town x years after 2010?

A. p = 13,400(1.045)x

B. p = 13,400(4.5)x

C. p = 13,400(1.045x)

D. p = 13,400 +4.5x

50. Mrs. Hans buys a house for $150,000. The value of the house is expected to increase at a rate of 10% every year. Which graph best represents the value of the house after x years?

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A.

B.

C.

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D.

51. A plane takes off from an airport, and minutes after takeoff the plane reaches a height of feet. Then, minutes after takeoff, the height of the plane has increased to feet. The plane is ascending at a constant rate during this time period. What is the equation that represents the rate, R, in feet per second, at which the plane is ascending?

52. Sandra’s cell phone plan gives her unlimited minutes for $15.50 per month. She is charged $0.08 for each text message, t. Which equation models the total monthly cost, C, for the cell phone?

A. C = 15.50t +0.08

B. C = 0.08t + 15.50

C. C = 15.58t

D. C = 15.42t

53. Kaitlyn is mowing her lawn. The lawn has an area of 5,625 square feet. She can mow about 75 square feet each minute. Which equation represents the amount of lawn, y, that Kaitlyn still has

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left to mow after x minutes?

A. y = 5,625 + 75x

B. y = 5,625 – 75x

C. y = 5,625(x – 75)

D. y = 5,625(75 – x)

54. Flash Air Conditioning charges

$65 for a service call on Monday through Thursday, plus $45 per hour for labor.

$75 for a service call on Friday through Sunday, plus $50 per hour for labor.

Perfect Air Conditioning charges

$40 for a service call on Monday through Thursday, plus $30 per hour for labor.

$60 for a service call on Friday through Sunday, plus $30 per hour for labor.

Flash advertises they will complete the same quality service in half the time it takes any company to complete the same job.The McCartney family had their air conditioner serviced last Saturday by Perfect Air Conditioning. According to a Flash advertisement, Flash would have finished the job (done by Perfect Air Conditioning) in half the time and charged the same total price for this service. How long did it actually take Perfect Air Conditioning to complete this service?

A. 1 hour 30 minutes

B. 3 hours

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C. 3 hours 20 minutes

D. 5 hours

55. Julie created the graph below.

Which equation best represents Julie's function?

A.

B.

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http://www.codecogs.com/eqnedit.php?latex=y%20=%202%5E%7Bx%7D@plus;3


C.

D.

56. An ice cream shop charges $1 for a cone and $2 per scoop of ice cream. Which equation models the cost of an ice cream cone, y, with x scoops of ice cream?

A. 1 = 2x + y

B. 2 = x + y

C. y = x + 2

D. y = 2x + 1

57. Nicholas borrowed $250 from his parents to buy a video game system. He has agreed to pay them back $15 each week. Which equation represents the amount of money Nicholas still owes his parents, p, after w weeks?

A. p = 250w – 15

B. p = 15w – 250

C. p = –15w + 250

D. p = 15(w – 250)

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58. Scientists measure the total population of sea turtles, y, each year in a refuge. They discovered an initial population of 65 sea turtles and an increase of 5 turtles each year. If x is the number of years after the initial observation, which equation best models the sea turtle population?

A. y = 5x + 65

B. y = 5(65)x

C. y = 65x + 5

D. y = 65(5)x

59. The number of bacteria, y, in a certain area doubles every hour, x. Which function could be used to model this situation?

A. y = x + 2

B. y = x2

C. y = 2x

D. y = 2x

60. Two solutions of salt water contain different percentages of salt. Solution A contains 20% salt, and solution B contains 40% salt.

Part A. Let x represent how many pints of solution A are used. Let y represent how many pints of solution B are used. Write an equation to represent the mix of x and y in order to create a solution containing 35%

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salt.

Part B. Graph the equation on the coordinate plane below to show the possible combinations, in pints, of solution A and solution B that will create a solution containing 35% salt.

Use words, numbers, and/or pictures to show your work.

61. In 6 years, Susan’s age, y, will be half as much as her sister’s age, x, will be in two years. Which equation models Susan’s age in terms of her sister’s age?

A.

B.

C.

D.

62. Steve and Marcia bought soda, chips, and gum.

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They bought twice as many chips as pieces of gum. They bought 3 fewer sodas than chips. Let P represent the total items purchased, s represent soda, c

represent chips, and g represent gum.

Which set of equations could be used to model the amounts of items purchased?

A. g = 2cs = c – 3P = s + c + g

B. c = 2gs = c – 3P = s + c + g

C. g = 2cs = c + 3P = s + c + g

D. c = 2gs = c + 3P = s + c + g

63. John has a full tank of gas in his car.

His car has a 15-gallon tank. His car gets 30 miles per gallon.

Which equation shows the relationship between how many miles, m, John drives and the number of gallons of gas, g, remaining in the car’s tank?

A.

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B.

C.

D.

64. Modeling with Equations

Part A. The drama club sold a total of 300 adult and student tickets to its upcoming show.

a. Write an equation that describes y, the number of adult tickets sold, in terms of x, the number of student tickets sold.

b. Graph your equation on a coordinate plane, showing all the possible combinations of adult and student tickets that could have been sold. Be sure to include appropriate labels and intervals on your graph.

Part B. A football is kicked a horizontal distance of 20 yards from a tee. During its flight, the ball reaches a maximum height of 10 yards above the ground.

a. Write an equation that models y, the height of the ball above the ground, in terms of x, its horizontal distance from the tee.

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b. Graph your equation on a coordinate plane, showing the entire path of the football. Be sure to include appropriate labels and intervals on your graph.

Part C. According to a report by the mayor’s office, the population of Star City is currently 24,000 residents, and the population is expected to grow at a rate of 3% per year.

a. Write an equation that predicts y, the population of the city, x years after the report was released.

b. Graph your equation on a coordinate plane, showing the projected population of Star City during the first 10 years after the report was released. Be sure to include appropriate labels and intervals on your graph.

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Part D. A local university has released a study that disagrees with the report by the mayor’s office. According to the university’s study, the population of Star City is currently 24,000 residents, but the population is expected to decrease at a rate of 2% per year.

a. Write an equation that models the university’s predictions. Let y represent the population of the city x years after the study was released.

b. Graph your equation on a coordinate plane, showing the projected population of Star City during the first 10 years after the study was released. Be sure to include appropriate labels and intervals on your graph.

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c. What are two reasons for the discrepancies in the data provided by the mayor’s office versus the data provided by the university’s study?

Explain your answer.

65. Andrew and Ryan spend a total of $44 at a state fair. There is an entrance fee of x dollars per person, and each ride costs $3.50. If they went on the same number of rides, which equation correctly represents this relationship, where n is the number of rides?

A.

B.

C.

D.

66. Tracey drops a ball from a height of 20 feet. During the first several bounces, the ball reaches a vertical height that is 75% of the

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preceding bounce height. If this pattern were to continue, write an equation that would represent h, the height of the ball, in feet, after n number of bounces.

67. The population of Austinberg on January 1, 2000 was 1.4 million. The population has decreased at a rate of 12% each year since. Which equation models the population (in millions), p, of Austinberg t years after January 1, 2000?

A. p = 1.4(0.12)t

B. p = 1.4(0.88)t

C. p = 1.4(1.12)t

D. p = 1.4(1.88)t

68. Nick deposited $500 in a bank that gives him 5% interest compounded annually. Which equation can be used to find the total amount, in T dollars, in Nick’s account after x years?

A.

B.

C.

D.

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