As part of a research project, you need to perform some population studies and find the followingdata: year 1980 1985 1990 1995 pop. (millions) 227.01 236.99 248.89 261.91From experience, you know that population models are more typically represented by exponential models (i.e.,P (t) = aebt) rather than linear models. However, since least squares is a linear approximation, we’ll improvise.Taking the log of both sides gives the linear equation,ln P (t) = ln(a) + bta) Using the data given above, find the least squares solution for the best fit exponential curve (i.e., find thebest approximation to ’a’ and ’b’).(b) Use your equation to approximate the population in 2010. As part of a research project, you need to perform some population studies and find the following data:| Year | Population (millions) ||------|-----------------------|| 1980 | 227.01 || 1985 | 236.99 || 1990 | 248.89 || 1995 | 261.91 |From experience, you know that population models are more typically represented by exponential models (i.e., \( P(t) = ae^{bt} \)) rather than linear models. However, since least squares is a linear approximation, we'll improvise. Taking the log of both sides gives the linear equation:\[\ln P(t) = \ln a + bt\](a) Using the data given above, find the least squares solution for the best fit exponential curve (i.e., find the best approximation to 'a' and 'b').(b) Use your equation to approximate the population in 2010.Hint: It would be best to not use the actual year but rather represent a given year by the number of years after 1980. Also, as a gauge, the actual population in 2010 was 309 million.

Answered: Image /qna-images/answer/39036cf7-fdf3-42a9-8e38-d4c3801f8fec.jpg

Answered: 4. data: As part of a research project,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

100%

As part of a research project, you need to perform some population studies and find the following
data:
year 1980 1985 1990 1995
pop. (millions) 227.01 236.99 248.89 261.91
From experience, you know that population models are more typically represented by exponential models (i.e.,
P (t) = ae^bt) rather than linear models. However, since least squares is a linear approximation, we’ll improvise.
Taking the log of both sides gives the linear equation,
ln P (t) = ln(a) + bt

a) Using the data given above, find the least squares solution for the best fit exponential curve (i.e., find the
best approximation to ’a’ and ’b’).

(b) Use your equation to approximate the population in 2010.