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SECONDARY MATH 1 // MODULE 2 LINEAR & EXPONENTIAL FUNCTIONS – 2.7H Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org 2.7H I Can See—Can’t You? A Solidify Understanding Task Kwan’s parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home in 2007 for $309,587. 1. Model the growth of the home’s value from 1997 to 2007 with both a linear and an exponential equation. Graph the two models below. Linear model: Exponential model: 2. What was the change in the home’s value from 1997 to 2007? The average rate of change is defined as the change in y (or f(x)) divided by the change in x. 3. What was the average rate of change of the linear function from 1997 to 2007? CC BY Andres Atehortua https://flic.kr/p/95abMF Homework help at www.rsgsupport.org 100

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Page 1: 2.7H I Can See—Can’t You?msubmathing.weebly.com/uploads/3/8/0/6/38068469/task_2.7.pdf · 2018-09-10 · A Solidify Understanding Task Kwan’s parents bought a home for $50,000

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.7H

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

2.7H I Can See—Can’t You?

A Solidify Understanding Task

Kwan’sparentsboughtahomefor$50,000in1997justasrealestatevaluesintheareastartedtorisequickly.Eachyear,theirhousewasworthmoreuntiltheysoldthehomein2007for$309,587.

1. Modelthegrowthofthehome’svaluefrom1997to2007withbothalinearandanexponentialequation.Graphthetwomodelsbelow.

Linearmodel:

Exponentialmodel:

2. Whatwasthechangeinthehome’svaluefrom1997to2007?

Theaveragerateofchangeisdefinedasthechangeiny(orf(x))dividedbythechangeinx.

3. Whatwastheaveragerateofchangeofthelinearfunctionfrom1997to2007?

CCBYAn

dresAteho

rtua

https://flic.kr/p/95abM

F

Homework help at www.rsgsupport.org 100

Page 2: 2.7H I Can See—Can’t You?msubmathing.weebly.com/uploads/3/8/0/6/38068469/task_2.7.pdf · 2018-09-10 · A Solidify Understanding Task Kwan’s parents bought a home for $50,000

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.7H

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

4. Whatistheaveragerateofchangeoftheexponentialfunctionintheintervalfrom1997to2007?

5. Howdotheaverageratesofchangefrom1997to2007compareforthetwofunctions?Explain.

6. Whatwastheaveragerateofchangeofthelinearfunctionfrom1997to2002?

7. Whatistheaveragerateofchangeoftheexponentialfunctionintheintervalfrom1997to2002?

8. Howdotheaverageratesofchangefrom1997to2002compareforthetwofunctions?Explain.

9. Howcanyouusetheequationoftheexponentialfunctiontofindtheaveragerateofchangeoveragiveninterval?Howdoesthisprocesscomparetofindingtheslopeofthelinethroughtheendpointsoftheinterval?

Homework help at www.rsgsupport.org 101

Page 3: 2.7H I Can See—Can’t You?msubmathing.weebly.com/uploads/3/8/0/6/38068469/task_2.7.pdf · 2018-09-10 · A Solidify Understanding Task Kwan’s parents bought a home for $50,000

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.7H

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

Considerthefollowinggraph:

10. Whatistheequationofthegraphshown?

11. Whatistheaveragerateofchangeofthisfunctionontheintervalfromx=-3tox=1?

12. Whatistheaveragerateofchangeofthisfunctionintheintervalfromx=-3tox=0?

13. Whatistheaveragerateofchangeofthisfunctionintheintervalfromx=-3tox=-1?

14. Whatistheaveragerateofchangeofthisfunctionintheintervalfromx=-3tox=-1.5?

Homework help at www.rsgsupport.org 102

Page 4: 2.7H I Can See—Can’t You?msubmathing.weebly.com/uploads/3/8/0/6/38068469/task_2.7.pdf · 2018-09-10 · A Solidify Understanding Task Kwan’s parents bought a home for $50,000

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.7H

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

15. Drawthelinethroughthepointatthebeginningandendofeachoftheintervalsin11,12,13and14.Whatistheslopeofeachoftheselines?

16. Whichoftheseaverageratesofchangebestrepresentsthechangeatthepoint(-2,4)?Explainyouranswer.

17. Howdoestheaveragerateofchangecomparetothechangefactorforanexponentialfunction?Whatisdescribedbyeachofthesequantities?

Homework help at www.rsgsupport.org 103

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