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

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

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

7. 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

8. Example 2-1a DOGS The 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. Age (mo.)4812 Weight (lb)152843 Remember: Time is most always the denominator 1/4 Rate of change = Write formula for rate change Final Weight - Start Weight Final Age - Start Age

9. Example 2-1a DOGS The 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. Age (mo.)4812 Weight (lb)152843 1/4 Rate of change = Final Weight - Start Weight Final Age - Start Age Rate of change = 43 - 28 lb 12 - 8 mo. Final Weight - Start Weight Final Age - Start Age Follow order of operations P E MD AS Use fraction bar as enclosure

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

11. Example 2-1c HEIGHTS The 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. Age (yr)6911 Height (in.)525860 Answer: 2 inches per year 1/4

12. Example 2-2a SCHOOLS The 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. Write formula for rate of change Rate of Change = Number final - number start Final year - starting year 2/4 Remember to put time in the denominator Rate of Change = 459 students 2002 459 students - 485 students 2002 - 1998 years 2002 2000

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

14. Example 2-2d SCHOOLS The 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

15. Example 2-3a TEMPERATURE The 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. 3/4 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

16. Example 2-3a TEMPERATURE The 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. 3/4 Need time period that temperature “did not change” 1 pm - 2 pm Answer: Look for a horizontal line Find time period on horizontal axis

17. Example 2-3c TEMPERATURE The 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

18. Example 2-4a TEMPERATURE The 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. Write the formula for the rate of change. Rate of Change = Final - Start Temp Final - Start Time 4/4 Find the rate of change from 1 P.M. to 2 P.M. Remember: Time is in the denominator

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

20. Example 2-4c TEMPERATURE The 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

21. End of Lesson 2 Assignment Lesson 4:2Rate of Change3 - 14 All