a.
To Find: The quadratic model for the data.
The
Given:
Year | ||||||||
Price |
Explanation:
Using the given data, determine the quadratic model.
Consider
To determine the coordinate system for the given data, arrange the data as the coordinates of the system.
Sketch the above coordinates in the coordinate system:
Calculate the quadratic regression with the above points and the degree
Thus, the quadratic formula obtained is:
b.
To Describe: The reasonable domain and range for your model.
The reasonable domain and range for the model is
Given:
Year | ||||||||
Price |
Explanation:
Describe the reasonable domain and range for your model:
In general,
The domain of the function is more appropriately defined as the period from
If the function has the negative parameter
Calculate the value
The price of the stamps never fell below
Thus, the reasonable domain and range for the model is
c.
To Estimate: The time when first-class postage was
By the end of
Given:
Year | ||||||||
Price |
Explanation:
Estimate the year the price of the stamps was
The quadratic model obtained from part
The given value of
Find the value of
Solve the quadratic equation using the Formula:
Substitute
The results of the analysis of
Initially,
d.
To Predict: When first-class postage will be
Based on this quadratic model, the stamp cannot cost
Given:
Year | ||||||||
Price |
Explanation:
Predict when first-class postage will be
The given value of
Find the value of
Solve the quadratic equation using the Formula:
Substitute
There is no real solution to this equation because the number under the root is negative.
In Part
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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