a.
To graph: The data given and the graph the model.
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Year | Bachelor’s degrees, B (in thousands) |
2005 | 826 |
2006 | 855 |
2007 | 875 |
2008 | 895 |
2009 | 916 |
2010 | 943 |
2011 | 982 |
2012 | 1026 |
2013 | 1053 |
2014 | 1068 |
2015 | 1082 |
2016 | 1099 |
The data can be approximated by the linear model
Graph:
By using the above data, points and the model can be plotted as
Interpretation:
The graph shows that the points plotted are very close to the graph of the linear model.
b.
To find: the bachelor’s degrees earned by women for each year from 2005 through 2016 by the linear model.
b.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
The linear model
Calculation:
Table below shows the data for each year from 2005 to 2016.
Year | Bachelor’s degrees, B (in thousands) |
2005 | 823 |
2006 | 849.42 |
2007 | 875.84 |
2008 | 902.26 |
2009 | 928.68 |
2010 | 955.1 |
2011 | 981.52 |
2012 | 1007.94 |
2013 | 1034.36 |
2014 | 1060.78 |
2015 | 1087.2 |
2016 | 1113.62 |
c.
To compare: the given data with the data obtained from linear model.
c.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Year | Bachelor’s degrees, B (in thousands) |
2005 | 826 |
2006 | 855 |
2007 | 875 |
2008 | 895 |
2009 | 916 |
2010 | 943 |
2011 | 982 |
2012 | 1026 |
2013 | 1053 |
2014 | 1068 |
2015 | 1082 |
2016 | 1099 |
The data can be approximated by the linear model
Calculation:
Year | Bachelor’s degrees, B (in thousands)
(data given) | Bachelor’s degrees, B (in thousands)
(data from the linear model ) | Difference between the two values |
2005 | 826 | 823 | 3 |
2006 | 855 | 849.42 | 5.58 |
2007 | 875 | 875.84 | -0.84 |
2008 | 895 | 902.26 | -7.62 |
2009 | 916 | 928.68 | -12.68 |
2010 | 943 | 955.1 | -12.1 |
2011 | 982 | 981.52 | 0.48 |
2012 | 1026 | 1007.94 | 18.06 |
2013 | 1053 | 1034.36 | 18.64 |
2014 | 1068 | 1060.78 | 7.22 |
2015 | 1082 | 1087.2 | -5.2 |
2016 | 1099 | 1113.62 | -14.62 |
As can be seen from the table, the difference between the given data and the data obtained from the linear model is very less thus; the model is best suited for the data.
d.
To find: the slope and the y -intercept of the model.
d.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
The linear model:
Concept used; The equation of a straight line is given by
Calculation:
We have the equation of linear model as
Thus the slope of the model is,
Slope tells how much the value of y changes with the change in x .
The y -intercept of the linear model shows the value at t = 0, as we know t = 5 corresponds to 2005, t = 0 will correspond to 2000. Thus the y -intercept gives the number of bachelor’s degrees earned by women in the year 2000.
e.
To find: the number of bachelor’s degrees earned by women in the year 2022
e.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
The linear model
Calculation:
t = 5 corresponds to 2005, therefore 2022 is given by t = 22,
Putting the value of t as 22 in the linear model we get,
Therefore, the number of bachelor’s degrees earned by women in the year 2022 is 1272.14 thousands
Chapter 1 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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