1. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model Data Storage on an MP3 Player and a DVD Using Linear Equations and Graphs Chapter 7

2. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Part 1

3. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model Data on an MP3 Player MP3 Players can be purchased with different amounts of memory, usually measured in Gigabytes (GB). Investigate Storage The number of songs that can be stored depends on how much memory is available. Determine a linear equation that models the relation between the number of songs stored and the memory available. 1GB = 1 000 000 000 bytes (B)

4. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. An advertisement for a popular MP3 player says that with 8 GB of memory, the device can store 1750 songs. With 32 GB, it stores 7000 songs. With 64 GB, it stores 14 000 songs. Songs vary in length. Claims such as these assume that an average song takes up about 4.5 Megabytes (4.5 MB) or 4 500 000 B of memory. Model Data on an MP3 Player Investigate Storage

5. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The data can be represented in a table of values. Create a table of values for the relation between the amount of memory and the number of songs in the MP3 player. Memory (GB) (x) Number of Songs (y) Model Data on an MP3 Player Create a Table of Values

6. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Memory (GB) (x) Number of Songs (y) 81750 327000 6414000 Model Data on an MP3 Player Create a Table of Values

7. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Represent the data on a graph. Model Data on an MP3 Player Create a Graph

8. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Represent the data on a graph. Model Data on an MP3 Player Create a Graph

9. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model Data on an MP3 Player Determine the Slope and y-intercept The slope is 218.75. The y-intercept is 0.

10. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The slope is 218.75. The y-intercept is 0. The equation is: Where x is amount of memory in gigabytes and y is the number of songs. Model Data on an MP3 Player Determine the Equation in Slope-Intercept Form

11. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Compare Storage Methods An MP3 player can store approximately 218.75 songs per GB of storage space. The equation that represents this situation is where x represents the storage space in GB, and y represents the number of songs stored. DVDs are another method of file storage.

12. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Compare Storage Methods Use the Slope-Intercept Form of an Equation A standard DVD has about 4.7 GB of storage space. Determine the number of songs that can be stored on a standard DVD using the equation from the previous problem.

13. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Compare Storage Methods Use the Slope-Intercept Form of an Equation The amount of memory, x, is 4.7 GB. Substitute this value into the equation. The equation is: A DVD can store approximately 1028 songs.

14. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Part 2

15. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Recordable DVDs hold 4.7 GB of data. The track starts 2.4 cm from the centre and finishes 5.8 cm from the centre. The data is written on a spiral track with a total length of about 12 km. Model Data on a DVD Investigate Data on a DVD

16. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Change 12 km to cm: Divide the number of bytes by the length in cm: There are 3917 bytes of data per cm of track. Change 4.7 GB to bytes: Model Data on a DVD Calculate the Amount of Data

17. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The inside loop has an average radius of 2.4 cm. The data stored on the inside loop is: There are 59 147 bytes of data on the inside loop. Calculate the circumference: Model Data on a DVD Calculate the Amount of Data on the Inside Loop

18. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The outside loop has an average radius of 5.8 cm. The data stored on the outside loop is: There are 142 579 bytes of data on the outside loop. Calculate the circumference: Model Data on a DVD Calculate the Amount of Data on the Outside Loop

19. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Distance from Centre (cm) (x) Data Stored (B) (x) Represent the distance from centre and the amount of data stored in a table of values. Model Data on a DVD Create a Table of Values.

20. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Distance from Centre (cm) (x) Data Stored (B) (y) 2.459 147 5.8142 579 Model Data on a DVD Create a Table of Values.

21. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model Data on a DVD Determine the Slope and the y-intercept The slope is 24 539 and the y-intercept is approximately 1.

22. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The distance from the centre in centimetres is x and the amount of data in bytes is y. This function is only defined for values of x from 2.4 to 5.8 cm. Model Data on a DVD Determine the Equation in Slope-Intercept Form The slope is 24 539. The y-intercept is approximately 1. The equation is:

23. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model Data on a DVD Use the Equation The amount of data stored in a loop on a DVD depends on the distance of the loop from the centre of the DVD. Where the distance from the centre in centimetres is x and the amount of data in bytes is y. The function is defined only for values of x from 2.4 to 5.8 cm. How much data is stored on the loop that is 3.5 cm from the centre? In the loop 3.5 cm from the centre, 85 887.5 B of data is stored.