Concept explainers
a.
To find: the logistic regression for the data.
a.
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 graph: the data in a
b.
Answer to Problem 31E
Explanation of Solution
Given information:
Calculation:
Scatter plot of the table data with
c.
To predict: the Pennsylvania population in the 2000 census.
c.
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 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.
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 find: what does the regression equation indicate about the population of Pennsylvania in the long run.
e.
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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