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Transparency 2. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 2-4c. Objective. Find rates of change. Example 2-4c. Vocabulary. Rate of change. A rate that describes how one quantity changes in relation to another. Example 2-4c.

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  1. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 2-4c Objective Find rates of change

  4. Example 2-4c Vocabulary Rate of change A rate that describes how one quantity changes in relation to another

  5. Example 2-4c Rate of Change Formula Final - Start Rate of change = Final - Start Then change to a unit rate (with denominator as 1)

  6. Lesson 2 Contents Example 1Find a Rate of Change Example 2Find a Negative Rate of Change Example 3Zero Rates of Change Example 4Zero Rates of Change

  7. Example 2-1a DOGSThe table below shows the weight of a dog in pounds between 4 and 12 months old. Find the rate of change in the dog’s weight between 8 and 12 months of age. Remember: Time is most always the denominator Write formula for rate change Final Weight - Start Weight Rate of change = Final Age - Start Age 1/4

  8. Example 2-1a DOGSThe table below shows the weight of a dog in pounds between 4 and 12 months old. Find the rate of change in the dog’s weight between 8 and 12 months of age. Final Weight - Start Weight Final Weight - Start Weight Rate of change = Final Age - Start Age Final Age - Start Age 43 - 28 lb Follow order of operations Rate of change = P E MD AS 12 - 8 mo. Use fraction bar as enclosure 1/4

  9. Example 2-1a Final Weight - Start Weight Rate of change = Final Age - Start Age 43 - 28 lb Use fraction bar as enclosure Rate of change = 12 - 8 mo. Subtract the numerator 15 lb Rate of change = Subtract the denominator 4 mo. Divide Rate of change = 3.75 Rate of change = 3.75 lb mo. Add dimensional analysis Answer: The dog grew an average of 3.75 pounds per month. 1/4

  10. Example 2-1c HEIGHTSThe table below shows Julia’s height in inches between the ages of 6 and 11. Find the rate of change in her height between ages 6 and 9. Answer: 2 inches per year 1/4

  11. Example 2-2a SCHOOLSThe graph to the right shows the number of students in the 8th grade between 1998 and 2002. Find the rate of change between 2000 and 2002. 2002 2000 Write formula for rate of change Remember to put time in the denominator Number final - number start Rate of Change = Final year - starting year 459 students 459 students - 485 students Rate of Change = 2002 2002 - 1998 years 2/4

  12. Example 2-2a Follow order of operations P E MD AS 459 – 485 students Use fraction bar as enclosure Rate of Change = 2002 – 2000 years Subtract the numerator -26 students Rate of Change = Subtract the denominator 2 years Divide Rate of Change = -13 students Rate of Change = -13 Add dimensional analysis year Answer: Rate of change = –13 students per year 2/4

  13. Example 2-2d SCHOOLSThe graph below shows the number of students in the 6th grade between 1997 and 2003. Find the rate of change between 2001 and 2003. Answer: –24 students per year 2/4

  14. Example 2-3a TEMPERATUREThe graph shows the temperature measured on each hour from 10 A.M. to 3 P.M. Find a time period in which the temperature did not change. Keys for reading a graph When line is rising, data is increasing When line is lowering, data is decreasing When line is horizontal, data is not changing 3/4

  15. Example 2-3a TEMPERATUREThe graph shows the temperature measured on each hour from 10 A.M. to 3 P.M. Find a time period in which the temperature did not change. Need time period that temperature “did not change” Look for a horizontal line Find time period on horizontal axis Answer: 1 pm - 2 pm 3/4

  16. Example 2-3c TEMPERATUREThe graph shows the temperature measured on each hour from 10 A.M. to 4 P.M. Find a time period in which the temperature did not change. Answer: 3 P.M. to 4 P.M. 3/4

  17. Example 2-4a TEMPERATUREThe graph shows the temperature measured on each hour from 10 A.M. to 3 P.M. Find the rate of change from 1 P.M. to 2 P.M. Find the rate of change from 1 P.M. to 2 P.M. Write the formula for the rate of change. Remember: Time is in the denominator Final - Start Temp Rate of Change = Final - Start Time 4/4

  18. Example 2-4a Find the rate of change from 1 P.M. to 2 P.M. Final - Start Temp Rate of Change = Final - Start Time Follow order of operations 62 62 - 62 degrees P E MD AS Rate of Change = 2 2 - 1 hours Subtract the numerator 0 degrees Subtract the denominator Rate of Change = 1 hour Divide Rate of Change = 0 Rate of Change = 0 degrees Add dimensional analysis hour Answer: Rate = 0ºF per hour 4/4

  19. Example 2-4c * TEMPERATUREThe graph shows the temperature measured on each hour from 10 A.M. to 4 P.M. Find the rate of change from 2 P.M. to 3 P.M. Answer: 3ºF 4/4

  20. End of Lesson 2 Assignment

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