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Objective

Find rates of change

Vocabulary

Rate of change

A rate that describes how one quantity changes in relation to another

Rate of Change Formula

Final - Start

Rate of change =

Final - Start

Then change to a unit rate

(with denominator as 1)

Example 1Find a Rate of Change

Example 2Find a Negative Rate of Change

Example 3Zero Rates of Change

Example 4Zero Rates of Change

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

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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

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.

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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

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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

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

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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

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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

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

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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

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

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

*

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

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Assignment