Suppose that the population of Velddrif, a small coastal town on the West Coast of South Africa, was 1000 at the end of the year 2000. Suppose further that the population increase. (continuously or steadily) by approximately 5% per year. Then the population can be described by the DE dP dt = 0.05P. Applying five iterations of the Improved Euler formula with P(0) = 1000, where t = 0 corresponds to the end of the year 2000, and a step size of h = 1 to this problem, yields (a) P(1) ≈ for the population size at the end of the year 2001.
Suppose that the population of Velddrif, a small coastal town on the West Coast of South Africa, was 1000 at the end of the year 2000. Suppose further that the population increase. (continuously or steadily) by approximately 5% per year. Then the population can be described by the DE dP dt = 0.05P. Applying five iterations of the Improved Euler formula with P(0) = 1000, where t = 0 corresponds to the end of the year 2000, and a step size of h = 1 to this problem, yields (a) P(1) ≈ for the population size at the end of the year 2001.
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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Transcribed Image Text:Suppose that the population of Velddrif, a small coastal town on the West Coast of South
Africa, was 1000 at the end of the year 2000. Suppose further that the population increased
(continuously or steadily) by approximately 5% per year. Then the population can be
described by the DE
dP
dt
= 0.05P.
Applying five iterations of the Improved Euler formula with P(0) = 1000, where t = 0
corresponds to the end of the year 2000, and a step size of h = 1 to this problem, yields
(a) P(1) ~
for the population size at the end of the year 2001.
(b) P(2) ≈
for the population size at the end of the year 2002.
Transcribed Image Text:(c) P(3) ≈
for the population size at the end of the year 2003.
(d) P(4) ≈
for the population size at the end of the year 2004.
(e) P(5)~
for the population size at the end of the year 2005.
4
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