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: US Census Bureau and UN. A suggested model to describe the population over time is: 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 x0 = 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: US Census Bureau and UN. A suggested model to describe the population over time is: 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 x0 = 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).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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