Concept explainers
To graph: The data of the table.
Answer to Problem 33E
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
Using graphing utility to find the graph of linear regression model and coefficient of determination.
The above graph show linear model of given data.
The model is
The coefficient of determination is 0.9786
To graph: The data of the table and find the power model.
Answer to Problem 33E
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
Using graphing utility to plot the points and draw the graph.
The above graph show power model of given data.
The model is
The coefficient of determination is 0.9438
To graph: The data of the table and find the exponential model.
Answer to Problem 33E
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
Using graphing utility to plot the points and draw the graph.
The above graph show exponential model of given data.
The model is
The coefficient of determination is 0.9866
To graph: The data of the table and find the logarithmic model.
Answer to Problem 33E
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
Using graphing utility to plot the points and draw the graph.
The above graph show logarithmic model of given data.
The model is
The coefficient of determination is 0.9289
To choose: The best fit model for given data.
Answer to Problem 33E
Exponential model
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
There are total four different model for same data with coefficient of determination.
Linear model,
Coefficient of determination,
Power model,
Coefficient of determination,
Exponential model,
Coefficient of determination,
Logarithmic model,
Coefficient of determination,
In all above model, the best coefficient of determination nearest to 1 for exponential model.
So, choose exponential model.
To predict: The populations of Luxembourg for the years 2014 through 2018.
Answer to Problem 33E
Exponential model
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
There are total four different model for same data with coefficient of determination.
Linear model,
Coefficient of determination,
Power model,
Coefficient of determination,
Exponential model,
Coefficient of determination,
Logarithmic model,
Coefficient of determination,
In all above model, the best choose exponential model.
To choose: The best model for population.
Answer to Problem 33E
Exponential model
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
There are total four different model for same data with coefficient of determination.
Linear model,
Coefficient of determination,
Power model,
Coefficient of determination,
Exponential model,
Coefficient of determination,
Logarithmic model,
Coefficient of determination,
In all above model, the best choose exponential model.
To verify: The choice of model for parts (e) and (g).
Answer to Problem 33E
Exponential model
Explanation of Solution
Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with
Yes, In both parts models same. That is exponential model.
Chapter 3 Solutions
Precalculus with Limits: A Graphing Approach
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