Concept explainers
a.
To draw: a
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Graph:
Interpretation:
The given plot shows that the budget for national defense has decreased approximately uniformly from 2011 up to 2015 and has been almost constant from 2015 to 2017 with small variations.
b.
To find: a quadratic model for the given data.
b.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Graph:
Interpretation:
Looking at the overall movement of graph, it appears almost following the quadratic model with small variation.
The equation of the graph comes out to be 1y13y
c.
To find: a quadratic model with the scatter plot from part (a).
c.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Graph:
Interpretation:
Looking at the overall movement of graph, it appears almost following the quadratic model with small variation.
d.
To find: the approximate spending on national defense each year using quadratic model of the data.
d.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Graph:
Interpretation:
From the graph the approximate spending on national defense in each year is given in following table
Conclusion:
Comparing the approximate data from the graph with the actual data, it is observed that the variation is not more than 10 at any instant.
Though the differences are substantial at some point, the quadratic model still fits much better than any other model because of how closely it follows the data.
Further, it can also be used to predict the future movement of the curve.
e.
To compare estimated data from the quadratic model with the actual data.
e.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
The estimated data and the actual data are given in the table below.
Actual data
Estimated data.
On a close observation of the difference between the estimated data and the actual data, it seems that nowhere the difference was more than 10, which is an indication of an almost fit model for the data.
The quadratic model follows closely with the movement of actual curve.
Thus, the model is good fit for the given data.
Conclusion:
Quadratic model is good fit for the data as the difference between two values is not constant but rather changes with almost constant proportion.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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