Deck 9: Modeling Data
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Deck 9: Modeling Data
1
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. Use the model to predict the percentage of these passengers who used a seat belt in 1998.
A) 59.9%
B) 69.3%
C) 47.2%

A) 59.9%
B) 69.3%
C) 47.2%
59.9%
2
If the prediction of the output value that you make based on the model is not possible or not reasonable __________ __________ occurred.
model breakdown
3
When you estimate an output value for an input value that is within the data input values by using the model you are doing __________.
interpolation
4
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. If you use the model to predict the percentage of these passengers who used a seat belt in 2017 which are you doing?
A) interpolation
B) extrapolation

A) interpolation
B) extrapolation
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5
Given the data set choose its scatterplot. Are the data approximately linear? 
A)
linear
B)
not linear
C)
linear
D)
not linear

A)

B)

C)

D)

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6
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. What is the slope of the model and what does it mean in terms of the problem?
A) 2.33. Every year seat belt use goes down 2.33.
B) 2.33. Every year seat belt use goes down 2.33%
C) 2.33. Every year seat belt use goes up 2.33%
D) 64.60. Seat belt use started at 64.60%

A) 2.33. Every year seat belt use goes down 2.33.
B) 2.33. Every year seat belt use goes down 2.33%
C) 2.33. Every year seat belt use goes up 2.33%
D) 64.60. Seat belt use started at 64.60%
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7
Decide which line fits the data best.
A)
B)
A)

B)

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8
Given the data set choose its scatterplot. Are the data approximately linear? 
A)
linear
B)
not linear
C)
linear
D)
not linear

A)

B)

C)

D)

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9
The __________ for a linear data set is the equation of the line which is the best fit for the data.
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10
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. If you use the model to predict the percentage of these passengers who used a seat belt in 2006 which are you doing?
A) interpolation
B) extrapolation

A) interpolation
B) extrapolation
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11
Decide which line fits the data best.
A)
B)
A)

B)

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12
When you estimate an output value for an input value that is outside the data input values by using the model you are doing __________.
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13
The percentage of eighth grade students P participating in school music or performing arts in the years from 1996 to 2006 may be modeled by
where t is years since 1996. Use the model to predict the percentage participation in 2020. Is this interpolation or extrapolation?
A) 74.69% interpolation
B) 74.69% extrapolation
C) 39.05% interpolation
D) 39.05% extrapolation

A) 74.69% interpolation
B) 74.69% extrapolation
C) 39.05% interpolation
D) 39.05% extrapolation
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14
The percentage of eighth grade students P participating in school music or performing arts in the years from 1996 to 2006 may be modeled by
where t is years since 1996. Use the model to predict the percentage participation in 2000. Is this interpolation or extrapolation?
A) 52.65% interpolation
B) 52.65% extrapolation
C) 58.09% interpolation
D) 58.09% extrapolation

A) 52.65% interpolation
B) 52.65% extrapolation
C) 58.09% interpolation
D) 58.09% extrapolation
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15
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. Use the model to predict the percentage of these passengers who used a seat belt in 2017.
A) 10.4%
B) 100%
C) 104.2%

A) 10.4%
B) 100%
C) 104.2%
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16
The percentage of eighth grade students P participating in school music or performing arts in the years from 1996 to 2006 may be modeled by
where t is years since 1996. What is the vertical intercept in the model? What does it mean?
A)
participation started at 55.37% in 1996
B)
participation goes up 55.37% each year since 1996
C)
participation will be zero in 2081
D)
participation will be zero in 2077

A)

B)

C)

D)

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17
The percentage of eighth grade students P participating in school music or performing arts in the years from 1996 to 2006 may be modeled by
where t is years since 1996. What is the horizontal intercept in the model? What does it mean? Is this extrapolation?
A)
participation started at 55.37% in 1996. not extrapolation
B)
participation goes up 55.37% each year since 1996. not extrapolation.
C)
participation will be zero in 2081. extrapolation
D)
participation will be zero in 2077. extrapolation

A)

B)

C)

D)

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18
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. Use the model to predict the percentage of these passengers who used a seat belt in 2005.
A) 75%
B) 76.3%
C) 47.4%

A) 75%
B) 76.3%
C) 47.4%
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19
The percentage of eighth grade students P participating in school music or performing arts in the years from 1996 to 2006 may be modeled by
where t is years since 1996. What is the slope in the model? What does it mean?
A)
participation started at 68% in 1996
B)
participation goes up 68% each year since 1996
C)
participation goes up 0.68% each year since 1996
D)
participation goes down 0.68% each year since 1996

A)

B)

C)

D)

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20
During the years 1994 to 2007 seat belt use among front seat passengers ages 16 to 24 has increased. A linear model for the percentage of these passengers who use a seat belt is
where P is percentage with a seat belt and t is years since 2000. The years before 2000 have a negative value for t. What is the vertical intercept of the model and what does it mean in terms of the problem?
A)
. In the year 1994 seat belt use was 64.60.
B)
. In the year 2000 seat belt use was 64.60.
C) 2.33. Every year seat belt use goes up 2.33%
D)
. In the year 2000 seat belt use was 64.60%.

A)

B)

C) 2.33. Every year seat belt use goes up 2.33%
D)

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21
The percentage P of 6 to 11 year old children in the U.S. who are overweight may be modeled by the equation
where t is years since 1980. What is the horizontal intercept of this model? Round to one decimal place. What does it mean for this application?

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22
Given the data set draw a scatterplot. Clearly label and scale the axes. Does the data set follow a linear pattern a parabolic pattern or neither? 
A)
linear
B)
parabolic
C)
neither
D)
parabolic

A)

B)

C)

D)

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23
Given the data set draw a scatterplot. Clearly label and scale the axes. Are the data approximately linear?


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24
The percentage P of 6 to 11 year old children in the U.S. who are overweight may be modeled by the equation
where t is years since 1980. Use the model to predict the percentage of 6 to 11 year old U.S. children who were overweight in 2000.

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25
During the years 2002 to 2008 smoking among twelfth grade students was declining. A linear model for the percentage of twelfth grade students who smoke is
. P is the percentage of twelfth graders who smoke and t is years since 2002. Find the vertical intercept of the model and explain its value in terms of the problem.

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26
The Supplemental Nutrition Assistance Program (SNAP) to provide food assistance has increased the number of participants in millions in the years from 2000 to 2008. Let P be the number of participants in millions and t be years since 2000. The following linear model fits the data:
. What is the horizontal intercept? Explain its value in terms of the problem if any.

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27
The Supplemental Nutrition Assistance Program (SNAP) to provide food assistance has increased the number of participants in millions in the years from 2000 to 2008. Let P be the number of participants in millions and t be years since 2000. The following linear model fits the data:
. Use the model to estimate the number of participants in SNAP in 2015. Is this interpolation or extrapolation?

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28
The Supplemental Nutrition Assistance Program (SNAP) to provide food assistance has increased the number of participants in millions in the years from 2000 to 2008. Let P be the number of participants in millions and t be years since 2000. The following linear model fits the data:
. What is the vertical intercept? Explain its value in terms of the problem.

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29
The Supplemental Nutrition Assistance Program (SNAP) to provide food assistance has increased the number of participants in millions in the years from 2000 to 2008. Let P be the number of participants in millions and t be years since 2000. The following linear model fits the data:
. Use the model to estimate the number of participants in SNAP in 2003. Is this interpolation or extrapolation?

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30
The Supplemental Nutrition Assistance Program (SNAP) to provide food assistance has increased the number of participants in millions in the years from 2000 to 2008. Let P be the number of participants in millions and t be years since 2000. The following linear model fits the data:
. What is the slope? Explain its value in terms of the problem.

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31
Given the data set draw a scatterplot. Clearly label and scale the axes. Are the data approximately linear?


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32
During the years 2002 to 2008 smoking among twelfth grade students was declining. A linear model for the percentage of twelfth grade students who smoke is
. P is the percentage of twelfth graders who smoke and t is years since 2002. Find the horizontal intercept of the model and explain its value in terms of the problem. Is this reasonable?

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33
During the years 2002 to 2008 smoking among twelfth grade students was declining. A linear model for the percentage of twelfth grade students who smoke is
. P is the percentage of twelfth graders who smoke and t is years since 2002. Use the model to predict the percentage of twelfth grade students who smoke in 2020. Is this answer reasonable?

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34
The population of the District of Columbia is given in the following table.
Draw a scatterplot and draw an eyeball best-fit line on the scatterplot.

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35
The percentage P of 6 to 11 year old children in the U.S. who are overweight may be modeled by the equation
where t is years since 1980. What is the vertical intercept of this model? What does it mean for this application?

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36
The percentage P of 6 to 11 year old children in the U.S. who are overweight may be modeled by the equation
where t is years since 1980. Use the model to predict the percentage of 6 to 11 year old U.S. children who will be overweight in 2020. Is this estimate reasonable?

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37
During the years 2002 to 2008 smoking among twelfth grade students was declining. A linear model for the percentage of twelfth grade students who smoke is
. P is the percentage of twelfth graders who smoke and t is years since 2002. Use the model to predict the percentage of twelfth grade students who smoke in 2010. Is this answer reasonable?

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38
The population of Florida is given in the following table.
Draw a scatterplot and draw an eyeball best-fit line on the scatterplot.

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39
Given the data set draw a scatterplot. Clearly label and scale the axes. Are the data approximately linear?


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40
During the years 2002 to 2008 smoking among twelfth grade students was declining. A linear model for the percentage of twelfth grade students who smoke is
. P is the percentage of twelfth graders who smoke and t is years since 2002. Find the slope of the model and explain the value of the slope in terms of the problem. Is percentage of twelfth graders who smoke going up or down over time?

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41
The average profit in dollars A that your baking business makes when baking n cakes is given by
. Find and explain the vertex.
A)
If you make 44 cakes you maximize your profit at $484.
B)
If you make 44 cakes you minimize your profit at $484.
C)
If you make 88 cakes you make no profit.

A)

B)

C)

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42
Given a quadratic model
where t is time the formula for the time of the vertex is
__________.


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43
A quadratic model for the median price of a condo is given by
. The variable x is the years since 2000. Use the model to predict the median price of a condo in 2005.
A) $300000
B) $195075
C) $305500

A) $300000
B) $195075
C) $305500
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44
The graph shows the average monthly high temperature in Newark NJ for months from November to April. If a quadratic model
is fit to the graphed data set will a be positive or negative? 
A) positive
B) negative


A) positive
B) negative
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45
The graph shows the average monthly high temperature in Newark NJ for months from April to September. If a quadratic model
is fit to the graphed data set will a be positive or negative? 
A) positive
B) negative


A) positive
B) negative
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46
The average profit in dollars A that your baking business makes when baking n cakes is given by
. How many cakes rounded to whole numbers should you bake in order to have a profit of $300?
A) 71 cakes
B) 17 cakes
C) 17 or 71 cakes

A) 71 cakes
B) 17 cakes
C) 17 or 71 cakes
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47
Given the data set draw a scatterplot. Clearly label and scale the axes. Does the data set follow a linear pattern a parabolic pattern or neither?


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48
The graph shows the average monthly high temperature in Newark NJ for months from November to April. If a quadratic model
is fit to the graphed data set estimate the coordinates of the vertex. 
A)
B)
C)
D)


A)

B)

C)

D)

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49
The graph shows the average monthly high temperature in Newark NJ for months from April to September. If a quadratic model
is fit to the graphed data set estimate the coordinates of the vertex. 
A)
B)
C)
D)


A)

B)

C)

D)

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50
Given the data set draw a scatterplot. Clearly label and scale the axes. Does the data set follow a linear pattern a parabolic pattern or neither? 
A)
linear
B)
parabolic
C)
neither
D)
parabolic

A)

B)

C)

D)

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51
The graph shows the average monthly high temperature in Newark NJ for months from April to September. Does the graph follow a linear pattern quadratic pattern or neither? 
A) linear
B) quadratic
C) neither

A) linear
B) quadratic
C) neither
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52
You are given a quadratic model
where t is time. If a is __________ the vertex identifies the minimum point.

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53
You are given a quadratic model
where t is time. If a is negative the vertex identifies the __________ point.

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54
The average profit in dollars A that your baking business makes when baking n cakes is given by
. Find and explain the vertical intercept.
A)
If you make 88 cakes you make no profit.
B)
If you make 88 cakes you maximize your profit.
C)
If you make no cakes you make no profit.

A)

B)

C)

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55
A quadratic model for the median price of a condo is given by
. The variable x is the years since 2000. Find the vertex of the model. Explain it in this problem.
A)
At the end of 2000 the median price is $338604.
B)
At the end of 2003 the median price is $338604.
C)
At the end of 2004 the median price is $338604.

A)

B)

C)

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56
Given the data set draw a scatterplot. Clearly label and scale the axes. Does the data set follow a linear pattern a parabolic pattern or neither?


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57
The graph shows the average monthly high temperature in Newark NJ for months from November to April. Does the data graphed follow a linear pattern a parabolic pattern or neither? 
A) linear
B) parabolic
C) neither

A) linear
B) parabolic
C) neither
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58
A __________ model fits data points that follow a parabolic pattern.
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59
Given the data set draw a scatterplot. Clearly label and scale the axes. Does the data set follow a linear pattern a parabolic pattern or neither?


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60
The average profit in dollars A that your baking business makes when baking n cakes is given by
. Find and explain the horizontal intercept(s).
A)
If you make no cakes you make no profit.
B)
If you make 44 cakes you minimize your profit at $484.
C)
and
If you make either 0 or 88 cakes you make no profit.

A)

B)

C)


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61
If a quadratic model
is fit to the graphed data set will a be positive or negative? 


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62
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. If a quadratic model
is fit to the graphed data set will a be positive or negative? 


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63
The average profit in dollars A that your baking business makes when baking n pies is given by
. Find and explain the vertical intercept.

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64
A quadratic model for the median home price in Tampa Florida is given by
. The variable x is the years since 2000. Find the vertex of the model. Explain it in this problem.

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65
The profit in dollars A that your baking business makes when baking n pies is given by
. Find the number of pies you must sell to have a profit of $300. Round to whole number(s).

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66
Does the data graphed follow a linear pattern a parabolic pattern or neither? 

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67
The profit in dollars A that your baking business makes when baking n pies is given by
. Find and explain the vertex.

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68
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. A quadratic model for this data is
where y is the average monthly high temperature and x is months after you moved to Chicago. Use the model to predict the lowest average monthly high temperature. Round to the nearest month to make this estimate. Round to one decimal place. 


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69
If a quadratic model
is fit to the graphed data set estimate the coordinates of the vertex. 


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70
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. A quadratic model for this data is
where y is the average monthly high temperature and x is months after you moved to Chicago. Use the model to predict the average monthly high temperature 2 months after you moved to Chicago. 


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71
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. A quadratic model for this data is
where y is the average monthly high temperature and x is months after you moved to Chicago. Use the model to predict the average monthly high temperature 8 months after you moved to Chicago. Round to one decimal place. 


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72
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. Does the graph show a linear pattern a quadratic pattern or neither? 

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73
A quadratic model for the median home price in Tampa Florida is given by
. The variable x is the years since 2000. Use the model to predict the median home price in the year 2008.

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74
You have moved to Chicago in the fall. The graph shows the average monthly high temperature for months since you moved to Chicago. If a quadratic model
is fit to the graphed data set estimate the coordinates of the vertex. 


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