1 The population of the world in the year 1650 was about 500 million and in the year 2010 was 6,756 million. (a) Assuming that the population of the world grows at a rate proportional to the population size, set up a differential equation and show why the population size y million at t years after 1650, is described by the function y(t) = 500ekt where k is the growth constant (you must find). (b) Use the function in (a) to predict the population in the year 2030. Is this answer realistic? Explain.

1 The population of the world in the year 1650 was about 500 million and in the year 2010 was 6,756 million. (a) Assuming that the population of the world grows at a rate proportional to the population size, set up a differential equation and show why the population size y million at t years after 1650, is described by the function y(t) = 500ekt where k is the growth constant (you must find). (b) Use the function in (a) to predict the population in the year 2030. Is this answer realistic? Explain.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4. The population of the world in the year 1650 was about 500 million and in the year 2010 was
6,756 million.
(a) Assuming that the population of the world grows at a rate proportional to the population
size, set up a differential equation and show why the population size y million at t years
after 1650, is described by the function y(t) = 500ekt where k is the growth constant (you
must find).
(b) Use the function in (a) to predict the population in the year 2030. Is this answer realistic?
Explain.

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