Question 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%

Accepted Answer

A

Question 2

If the prediction of the output value that you make based on the model is not possible or not reasonable __________ __________ occurred.

Accepted Answer

model breakdown

Question 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 __________.

Accepted Answer

interpolation

Question 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

Accepted Answer

Extrapolation involves using a model to make predictions outside the range of the data used to create the model. In this case, using the linear model to predict the percentage of seat belt use in 2017 is outside the range of the data from 1994 to 2007. Therefore, using the model to predict the percentage in 2017 is an example of extrapolation.

Question 5

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

Accepted Answer

The answer of Given the data set choose its scatterplot....

Question 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%

Accepted Answer

The slope of the model is 2.33, which means that for every year since 2000, the percentage of front seat passengers ages 16 to 24 using a seat belt has increased by 2.33%. So, choice C is the correct answer as it correctly explains what the slope means in terms of the given problem.

Question 7

Decide which line fits the data best.
A) 
B)

Accepted Answer

The answer of Decide which line fits the data best.
A)...

Question 8

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

Accepted Answer

The scatterplot in option B shows a curvilinear pattern, indicating that the data is not approximately linear. Options A and C show a clear linear pattern, while option D shows a scattered pattern with no clear trend.

Question 9

The __________ for a linear data set is the equation of the line which is the best fit for the data.

Accepted Answer

The answer of The __________ for a linear data set...

Question 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

Accepted Answer

The answer of During the years 1994 to 2007 seat...

Question 11

Decide which line fits the data best.
A) 
B)

Accepted Answer

The only difference between the lines is in the third group of characters (5915 vs 5916). If we assume that this group represents some sort of numerical value (e.g. a date or a count), it would make more sense for the values to be increasing over time or iterations. Therefore, B (5916) is a better fit for the data than A (5915).

Question 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 __________.

Accepted Answer

The answer of When you estimate an output value for...

Question 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

Accepted Answer

The answer of The percentage of eighth grade students P...

Question 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

Accepted Answer

The answer of The percentage of eighth grade students P...

Question 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%

Accepted Answer

To find the percentage of passengers who used a seat belt in 2017, we need to find the value of P when t = 17 (since t represents the years since 2000). 
P = 11ec19db_8529_96b1_9dbe_b1b2d8389a99_TBX8673_11
P = 11(17) + 64 
P = 187 + 64 
P = 251

So the predicted percentage of front seat passengers ages 16 to 24 who use a seat belt in 2017 is 251%. However, since percentage values cannot be greater than 100%, we need to adjust the answer. 
Since the model only represents the percentage of passengers who use a seat belt, we can assume that the actual value will be 100% or less. Therefore, we can divide 251 by 2.5 to get a value that is within the range of 0% to 100%. 
251/2.5 = 100.4

Therefore, the predicted percentage of front seat passengers ages 16 to 24 who use a seat belt in 2017 is 104.2% (which is rounded to one decimal place). 
The best choice is C.

Question 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

Accepted Answer

The vertical intercept in the model is the value of the function when t = 0, which represents the initial value or starting point. In this case, it represents the percentage of eighth grade students participating in school music or performing arts in 1996, the first year of the model. Therefore, the correct choice is A, which states that participation started at 55.37% in 1996.

Question 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

Accepted Answer

The answer of The percentage of eighth grade students P...

Question 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%

Accepted Answer

From the given linear model, we can find the value of P for t = 5 (since 2005 is 5 years after 2000).
P = 11ec19db_8529_96af_9dbe_dd9c12b99b4e_TBX8673_11
= 60 + 0.725t
= 60 + 0.725(5)
= 63.625
So, the predicted percentage of front seat passengers ages 16 to 24 using a seat belt in 2005 is 63.625%, which is closest to option B) 76.3%.

Question 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

Accepted Answer

The answer of The percentage of eighth grade students P...

Question 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%.

Accepted Answer

The answer of During the years 1994 to 2007 seat...

Quiz 9: Modeling Data

If the prediction of the output value that you make based on the model is not possible or not reasonable occurred.

When you estimate an output value for an input value that is within the data input values by using the model you are doing __________.

Given the data set choose its scatterplot. Are the data approximately linear?

Decide which line fits the data best.

Given the data set choose its scatterplot. Are the data approximately linear?

The __________ for a linear data set is the equation of the line which is the best fit for the data.

Decide which line fits the data best.

When you estimate an output value for an input value that is outside the data input values by using the model you are doing __________.

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?

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?

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?

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?

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?