1ACE Exercise 10. Name Date Class

Transcription

1 1ACE Exercise 10 Investigation Make a table and a graph of (time, temperature) data that fit the following information about a day on the road: We started riding at 8 a.m. The day was quite warm, with dark clouds in the sky. About midmorning, the temperature dropped quickly to 63 and there was a thunderstorm for about an hour. After the storm, the sky cleared and there was a warm breeze. As the day went on, the sun steadily warmed the air. When we reached our campground at 4 p.m. it was 89 F. HINT There is no one right answer. Time and Temperature may not be exact numbers in this problem, so you will need to use the clues to make reasonable estimates. A Day on the Road A Day on the Road Time (x) 8 A.M. 9 A.M. Temperature F (y) quite warm º A.M. (midmorning) 11 A.M. 12 P.M. 1 P.M. 2 P.M. Temperature (ºF) P.M. 0 8 A.M. 9 A.M. 10 A.M. 11 A.M. 12 P.M. 1 P.M. 2 P.M. 3 P.M. 4 P.M. 4 P.M. Time (h) 67

2 2ACE Exercise 2 Investigation 2 2. Dezi researches DVD rental prices at local video stores. Source Video has a yearly membership package. The manager gives Dezi this table: Source Video Membership/Rental Packages Number of DVDs Rented Total Cost $30 $35 $40 $45 $50 $55 $60 HINT Sketch a graph for Source Video. What value should be on the x-axis? What value should be on the y-axis? What should be the scale for each axis?

3 2ACE Exercise 2 (continued) Supreme Video does not have membership packages. Dezi makes the graph below to relate the cost at Supreme Video to the number of DVDs rented. Investigation 2 Rental Cost $100 $80 $60 $40 y Supreme Video DVD Rentals $20 x $ Number of DVDs HINT Make a table for Supreme Video. Supreme Video Membership/Rental Packages Number of DVDs Rented Total Cost $0 a. Both video stores have a good selection of movies. Dezi's family plans to watch about two movies a month. Which video store should they choose? b. Write a paragraph explaining to Dezi how he can decide which video store to use. c. For each store, describe the pattern of change relating the number of DVDs rented to the cost. 69

4 3ACE Exercise 8 Investigation 3 8. Sean is buying a new DVD player and speakers for $315. The store offers him an interest-free payment plan that allows him to pay in monthly installments of $25. HINT Completing the table may help you answer the questions. Payment Plan Number of Payments (n) Amount Still Owed (a) $290 a. How much will Sean still owe after one payment? HINT Each monthly payment is $25. The cost is $315. $315 $25 = $290. Sean will still owe $290 after 1 payment. a. After two payments? a. After three payments? b. Use n to stand for the number of payments and a for the amount still owed. Write an equation for calculating a for any value of n. b. a = 70

5 3ACE Exercise 8 (continued) Investigation 3 c. Use your equation to make a graph showing the relationship between n and a. HINT You already completed a table. d. As n increases by 1, how does a change? d. How is this change shown in the table? d. How is it shown on the graph? e. How many payments will Sean have to make in all? d. How is this shown in the table? d. How is this shown on the graph? 71

6 4ACE Exercise 5 Investigation 4 5. The Mudville Manatees won the league baseball championship. The manager of the souvenir shop wants to order special shirts and caps to sell to fans. She does market research and predicts these relationships between price in dollars p and number sold n: Shirts: n = 5, p Caps: n = 3, p Use these equations to answer the questions below. Making calculator tables and graphs might help. a. What are the projected shirt sales if the price is $20 per shirt? HINT How many shirts will be sold if the price is $10 per shirt? n = 5, p n = 5,000 (150 10) n = 5,000 1,500 n = 3,500 3,500 shirts will be sold at $10. b. Suppose the manager wants to sell 3,500 shirts (n). How much should she charge for each shirt? HINT What price per shirt will lead to the sale of 500 shirts? n = 5, p 500 = 5, p 150p = 5, p = 4,500 4,500 p = 150 p = 30 A price of $30 per shirt will lead to the sale of 500 shirts. 72

7 4ACE Exercise 5 (continued) Investigation 4 c. What are the projected cap sales if the price is $17 per cap? d. Suppose the manager wants to sell 1,800 caps (n). How much should she charge for each cap? HINT What price per shirt will lead to the sale of 2,500 caps? n = 3, p 2,500 = 3, p 100p = 3, p = 500 p = 5 A price of $5 per cap will lead to the sale of 2,500 caps. 73

8 Unit Test 1. The tour operators thought it would be a good idea to get a souvenir T-shirt for each customer who went on the Ocean Bike Tour. They found a company who would sell them shirts with their logo for $6.00. a. Make a table and a graph that show number of shirts (x) and cost (C). T-shirt Cost x C b. Would it make sense to connect the points on your graph with a line? Why or why not? c. Write an equation using symbols to determine the T-shirt cost (C) for any number of customers (x). 74

9 Unit Test (continued) 2. Write a story that would describe this graph. Money Time 3. The number of hours of daylight in a day changes throughout the year. We say that the days are shorter in winter and longer in summer. The following table shows the number of daylight hours in Chicago, Illinois on a typical day during each month of the year (January is month 1, and so on). Describe the pattern relating the month and the number of daylight hours. HINT Make a graph. Average Daylight per Day Average Daylight per Day Month 1 (January) 2 (February) 3 (March) Daylight Hours Month Daylight Hours 75

10 Unit Test (continued) 4. Dee bought a compact disc player with the money he earned working during his vacation. He checked some stores to find the cheapest place to buy CDs. Taylor's Department Store sells CDs for $15.50 each. Buyer's Warehouse has an initial $25 membership fee to shop there, then each CD would cost $12. a. Make a table for the cost for any number of CDs at each store. b. Write an equation using symbols to determine the cost (C) for any number (n) of CDs at each store. a. Taylor's Department Store: a. Buyer's Warehouse: c. How many CDs would Dee have to purchase to have Buyer's Warehouse be the best place to buy CDs? Show your work. d. How many CDs would Dee have to purchase to have Taylor's Department Store be the best place to buy CDs? Show your work. 76

11 Unit Test (continued) 5. The drawings below show a series of dot figures. Figure 1 Figure 2 Figure 3 Figure 4 a. Make a table showing the number of dots needed to make Figures Figure (n) Number of dots (d ) 3 b. Write an equation showing the number of dots d needed to make any Figure n. 77