PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 7, Problem 71RE
Solution
a.
To calculate: The linear regression equation for the population of Hawaii.
The obtained matrix is
Given Information:
The table is defined,
| Time (years) | Hawaii (thousands) | Idaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Calculation:
Consider the given table,
| Time (years) | Hawaii (thousands) | Idaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Use a graphing calculator to find the linear rgeression.
Step 1. Insert the table in calculator by using the table feature.
Step 2. Use the LinReg feature with first two list
And,
Therefore, the obtained equation is
b.
To calculate: The linear regression equation for the population of Ladho.
The obtained model is
Given Information:
The table is defined,
| Time (years) | Hawaii (thousands) | Ldaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Calculation:
Consider the given table,
| Time (years) | Hawaii (thousands) | Ldaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Use a graphing calculator to find the logestic model.
Step 1. Insert the table in calculator by using the table feature.
Step 2. Use the LinReg feature with first two list
Hence, the obtained result is
c.
To Graph: The models in parts (a) and (b) and use these models to explain when the populations of the two states were about the same.
The obtained graph is defined as,
Given Information:
The table is defined,
| Time (years) | Hawaii (thousands) | Ldaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Calculation:
Consider the given table,
| Time (years) | Hawaii (thousands) | Ldaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Use a graphing calculator to find the logestic model.
Step 1. Insert the table in calculator by using the table feature.
Step 2. Graph the both equations (a) and (b) then use the intersect feature to find the intersection point.
The x -coordinates of the point of intersection is 10.2, and it is representing year 1990.
Hence, the obtained years is 1990.
d.
To determine: The models, which appears to be a better fit for the data and explain which model would you choose to make predictions beyond 2020
Hawaii is having a linear model and Idaho population is having exponential or logistic
Given Information:
The table is defined,
| Time (years) | Hawaii (thousands) | Ldaho (thousands) |
| 1980 | 965 | 944 |
| 1990 | 1108 | 1007 |
| 2000 | 1212 | 1294 |
| 2010 | 1360 | 1568 |
Calculation:
Consider the given information,
The linear model seems to be a good fit for Hawaii as most points appear to be on the line which means that there is almost a constant change in population.
An exponential or a logistic model seems to be appropriate for Idaho since there is a sudden increase in population for the same year intervals which is from 1990 to 2000.
Hence, Hawaii is having a linear model and Idaho population is having exponential or logistic
Chapter 7 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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