Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Question
Chapter 5.3, Problem 31E
a.
To determine
To find: the logistic regression for the data.
a.
Expert Solution
Answer to Problem 31E
Explanation of Solution
Given information: Table shows the population of Pennsylvania in each 10 years
between 1830 and 1950.
| Year since 1820 | Population in Thousands |
| 10 | 1348 |
| 20 | 1724 |
| 30 | 2312 |
| 40 | 2906 |
| 50 | 3522 |
| 60 | 4283 |
| 70 | 5258 |
| 80 | 6302 |
| 90 | 7665 |
| 100 | 8720 |
| 110 | 9631 |
| 120 | 9900 |
| 130 | 10,498 |
Calculation:
The logistic regression curve, for population P, t years after 1820 as produced by graphing utility:
b.
To determine
To graph: the data in a
b.
Expert Solution
Answer to Problem 31E
Explanation of Solution
Given information:
Calculation:
Scatter plot of the table data with
c.
To determine
To predict: the Pennsylvania population in the 2000 census.
c.
Expert Solution
Answer to Problem 31E
Explanation of Solution
Given information:
Calculation:
2000 is 180 years after 1820, so t = 180 plug that into the regression equation to find the Pennsylvania population in the 2000 census.
d.
To determine
To find: in what year was the Pennsylvania population growing the fastest and what significant behavior does the graph of the regression equation exhibit at that point
d.
Expert Solution
Answer to Problem 31E
About year 1900.
Explanation of Solution
Given information:
Calculation:
Scatter plot of the table data with
From the graph, the population is increasing the fastest around t =80 .or the year 1900.
The slope of the tangent line at that point is greatest there, in other words, the change in population over the change in time is largest.
The concavity also changes at that point, so it is a point of inflection.
e.
To determine
To find: what does the regression equation indicate about the population of Pennsylvania in the long run.
e.
Expert Solution
Answer to Problem 31E
In the long term, the equation says the population will stabilize at around 12.66 million.
Explanation of Solution
Given information:
Calculation:
So, in the long term, the equation says the population will stabilize at around 12.66 million.
Chapter 5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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