Concept explainers
a.
Use a graphical utility to create a sactter plot of the data.
a.
Answer to Problem 23PS
The
Explanation of Solution
Calculation:
The scatter plot of the data is given as
Hence, the graph is shown above.
b.
Decide the model for data .
b.
Answer to Problem 23PS
logarithmic model.
Explanation of Solution
Calculation:
The best model for these points is logarithmic model
Hence, the data could be modelled by a logarithmic model
c.
Explain the model of part
c.
Answer to Problem 23PS
From the graph, we can see that points are increasing non-linearly, so, we cannot use a model linear model for this. We can also see that points are not growing rapidly,so, exponential model is not suitable.
Explanation of Solution
Calculation:
From the graph, we can see that points are increasing non-linearly, so, we cannot use a model linear model for this. We can also see that points are not growing rapidly,so, exponential model is not suitable.
Hence, we chose logarithmic model.
d.
find the model you chose in part (b) for the data and graph the model with scatter plot.
d.
Answer to Problem 23PS
Explanation of Solution
Calculation:
Now, by using the values of and from the data and graphing utility we get,
Hence, the required model is
Now, the graph of scatter plot is,
Hence, the graph is shown above.
e.
Determine if the model you chose fits the data.
e.
Answer to Problem 23PS
From the graph we can see that the model we get fits the data very well.
Explanation of Solution
Calculation:
From the graph we can see that the model we get fits the data very well.
Hence, logarithmic model fits the data very well.
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning