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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

Rate of change =

Then change to a unit rate

(with denominator as 1)

Final - StartFinal - Start

Example 1 Find a Rate of Change

Example 2 Find a Negative Rate of Change

Example 3 Zero Rates of Change

Example 4 Zero Rates of Change

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.) 4 8 12

Weight (lb) 15 28 43

Remember: Time is most always the denominator

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Rate of change =

Write formula for rate change

Final Weight - Start Weight

Final Age - Start Age

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.) 4 8 12

Weight (lb) 15 28 43

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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 operationsP E MD AS

Use fraction bar as enclosure

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Rate of change =Final Weight - Start WeightFinal Age - Start Age

Rate of change =43 - 28 lb12 - 8 mo.

Use fraction bar as enclosure

Rate of change =Subtract the numerator

15 lbSubtract the denominator4 mo.

DivideRate of change = 3.75 Add dimensional analysis

Answer: The dog grew an average of 3.75 pounds per month.

Rate of change = 3.75 lbmo.

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) 6 9 11

Height (in.) 52 58 60

Answer: 2 inches per year

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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 startFinal year - starting year

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Remember to put time in the denominator

Rate of Change = 459 students 2002

459 students - 485 students 2002 - 1998 years

20022000

459 – 485 students2002 – 2000 years

-26 students2 years

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Rate of Change =

Follow order of operationsP E MD AS

Use fraction bar as enclosure

Subtract the numerator

Rate of Change = Subtract the denominator

Divide

Rate of Change = -13 Add dimensional analysisRate of Change = -13 studentsyear

Answer: Rate of change = –13 students per year

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

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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.

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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

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.

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Need time period that temperature “did not change”

1 pm - 2 pmAnswer:

Look for a horizontal line

Find time period on horizontal axis

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.

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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 TempFinal - Start Time

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Find the rate of change from 1 P.M. to 2 P.M.

Remember: Time is in the denominator

62 2

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Rate of Change =Final - Start TempFinal - 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 operationsP E MD AS

Subtract the numerator

Rate of Change = 0 degrees Subtract the denominator1 hour

Divide

Rate of Change = 0 Add dimensional analysisRate of Change = 0 degrees hour

Answer: Rate = 0ºF per hour

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

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Assignment

Lesson 4:2 Rate of Change 3 - 14 All