The world population over a period of 250 years has been estimated by the U.N. (see table below). Year Population [billion] 1800 1.00 1850 1.30 1900 1.70 1950 2.50 1970 3.70 1990 5.30 2005 6.50 2020 7.60 2050 9.10* *) prediction Source: U.S Census Bureau and UN. A suggested model to describe the population over time is: P= L 1+ e-k(x-xo) Where p is the population, x is the year and L, k and x, are constants. I represents the all time maximum of the population. a) Fit the model to the data using non-linear regression using initial guesses L = 20, k = 0.01 and x) = 2050. What will be the all time maximum of the world population according to this model? b) Find the coefficient of determination (R²) for the fit. (If you did not answer question a), you may use the initial guesses as parameter values).
The world population over a period of 250 years has been estimated by the U.N. (see table below). Year Population [billion] 1800 1.00 1850 1.30 1900 1.70 1950 2.50 1970 3.70 1990 5.30 2005 6.50 2020 7.60 2050 9.10* *) prediction Source: U.S Census Bureau and UN. A suggested model to describe the population over time is: P= L 1+ e-k(x-xo) Where p is the population, x is the year and L, k and x, are constants. I represents the all time maximum of the population. a) Fit the model to the data using non-linear regression using initial guesses L = 20, k = 0.01 and x) = 2050. What will be the all time maximum of the world population according to this model? b) Find the coefficient of determination (R²) for the fit. (If you did not answer question a), you may use the initial guesses as parameter values).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The world population over a period of 250 years has been estimated by the U.N. (see table below).
Year
Population
[billion]
1800
1.00
1850
1.30
1900
1.70
1950
2.50
1970
3.70
1990 5.30
2005
6.50
2020
7.60
2050
9.10*
*) prediction
Source: U.S Census Bureau
and UN.
A suggested model to describe the population over time is:
P=
L
1+ e-k(x-xo)
Where p is the population, x is the year and L, k and x, are constants. I represents the all time maximum of the
population.
a) Fit the model to the data using non-linear regression using initial guesses L = 20, k = 0.01 and x) = 2050.
What will be the all time maximum of the world population according to this model?
b) Find the coefficient of determination (R²) for the fit.
(If you did not answer question a), you may use the initial guesses as parameter values).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14d6463f-459a-4ff8-9e35-e4b6b668ec4f%2Fff96788d-f7d9-4a68-a156-51607e9cb26e%2F5dzey3e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The world population over a period of 250 years has been estimated by the U.N. (see table below).
Year
Population
[billion]
1800
1.00
1850
1.30
1900
1.70
1950
2.50
1970
3.70
1990 5.30
2005
6.50
2020
7.60
2050
9.10*
*) prediction
Source: U.S Census Bureau
and UN.
A suggested model to describe the population over time is:
P=
L
1+ e-k(x-xo)
Where p is the population, x is the year and L, k and x, are constants. I represents the all time maximum of the
population.
a) Fit the model to the data using non-linear regression using initial guesses L = 20, k = 0.01 and x) = 2050.
What will be the all time maximum of the world population according to this model?
b) Find the coefficient of determination (R²) for the fit.
(If you did not answer question a), you may use the initial guesses as parameter values).
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