a.
To determine: The logistic regression model and find the population in 2016 of U.S.
The obtained population is
Given Information:
The table is defined as,
Year | Population |
1900 | |
1910 | |
1920 | 106 |
1930 | |
1940 | |
1950 | |
1960 | |
1970 | |
1980 | |
1990 | |
2000 | |
2010 | |
2016 |
Calculation:
Consider the given polynomial,
Using a graphing calculator, enter the year values starting from
Step 1. Press the tables’ option and enter the values as mentioned above.
Step 2. Use the Logistic feature to find the logistic regression model.
Display values are following as,
Thus, the function can be written as following,
Substitute 116 for t to find the population in 2020 as
Therefore, the population in 2016 is
b.
To compare: The prediction with the listed values in the table for 2016
The prediction is an overestimation is
Given Information:
The table is defined as,
Year | Population |
1900 | |
1910 | |
1920 | 106 |
1930 | |
1940 | |
1950 | |
1960 | |
1970 | |
1980 | |
1990 | |
2000 | |
2010 | |
2016 |
Explanation:
Consider the given information,
The obtained values for year 2016 in part (a) is
Hence, the prediction is an overestimation is
c.
To determine: The better prediction model between exponential or logistic model.
The logistic model is better model.
Given Information:
The table is defined as,
Year | Population |
1900 | |
1910 | |
1920 | 106 |
1930 | |
1940 | |
1950 | |
1960 | |
1970 | |
1980 | |
1990 | |
2000 | |
2010 | |
2016 |
Explanation:
Consider the given information,
The logistic model gave a much closer prediction to the actual value in 2016 so it is better than the exponential model from Example 6.
Therefore, the logistic model is better model.
Chapter 3 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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