Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Question

Chapter 5, Problem 41RE

To determine

To find: the logistic regression for the data.

Expert Solution

Answer to Problem 41RE

P=12655.17381+12.87142e−0.03250t .

Explanation of Solution

Given information: Table shows the growth of the U.S. population from 1790 to 2000 in 30- year’s increments and indicates the growth in 2010.

Year	Growth
1790	3929
1820	9638
1850	23,192
1880	50189
1910	92,228
1940	132,165
1970	203,302
2000	281,422
2010	309,447

Calculation:

The logistic regression curve, for population P, t years after 1820 as produced by graphing utility:

P=1633001.591+17.471e−0.06378t .

To determine

To graph: the data in a scatter plot and super impose the regression curve.

Expert Solution

Answer to Problem 41RE

Explanation of Solution

Given information: P=1633001.591+17.471e−0.06378t

Calculation: Let t = 0 for 1970 then the above table would be written as.

Year ( t)	Growth ( P)
0	3929
30	9638
60	23,192
90	50189
120	92,228
150	132,165
180	203,302
210	281,422
220	309,447

Scatter plot of the table data shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 41RE , additional homework tip 1

To determine

To predict: the U.S. population in the 2050.

Expert Solution

Answer to Problem 41RE

P(260)≈1632999.79 thousands.

Explanation of Solution

Given information: P=1633001.591+17.471e−0.06378t

Calculation:

P=1633001.591+17.471e−0.06378t .

2050 is 260 years after 1970, so t = 260 plug that into the regression equation to find the U.S. population in the 2050.

P(260)=1633001.591+17.471e−0.06378×260≈1632999.79.P(260)≈1632999.79 thousands.

To determine

To find: in what year was the U.S. population growing the fastest and what significant behavior does the graph of the regression equation exhibit at that point

Expert Solution

Answer to Problem 41RE

About year 2000.

Explanation of Solution

Given information: P=1633001.591+17.471e−0.06378t .

Calculation:

Scatter plot of the table data shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 41RE , additional homework tip 2

From the graph, the population is increasing the fastest around t =210 .or the year 2000.

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.

To determine

To find: what does the regression equation indicate about the population of Pennsylvania in the long run.

Expert Solution

Answer to Problem 41RE

In the long term, the equation says the population will stabilize at around 1633001.59 .

Explanation of Solution

Given information: P=1633001.591+17.471e−0.06378t

Calculation:

limt→∞P=1633001.591+17.471e−0.06378t=1633001.59 .

So, in the long term, the equation says the population will stabilize at around 1633001.59

Chapter 5, Problem 40RE

Chapter 5, Problem 42RE

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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