
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Direction: Answer Part I to III, show your complete and detailed solution in typewritten.

Transcribed Image Text:Part I: Using the given data, follow the algorithm below to create a mathematical model which describes the
population growth for the region.
REGION
Central Visayas
a) Compute the difference D in population during the following year intervals: 1990-2000; 2000-
2010: and 2010-2020.
b)
Use the formula below to get the rate of growth R of each year interval: Let R1990-2000 be the
relative growth rate of the 1990-2000 year interval. Its formula is defined as
D1990-2000
R1990-2000
P2000
where D1990-2000 is the difference of the population in 1990 and 2000; and P1990 is the population
in 1990. (Express answers in this part in four decimal places).
c) Find the average (arithmetic mean) of the three rates then divide it by 10. The result will serve as
the annual relative growth rate r of the region's population. Express this in four decimal places.
R1990-2000 + R2000-2010 + R2010-2020
3
10
1990
4,740,318
POPULATION
r =
2000
5,706,953
2010
6,800,180
2020
8,081,988
d)
Let t=0 be year 1990, prepare the model for the population growth of your assigned region using
the continuous exponential model C(t) = Poet.
e) Use answer in letter d to estimate the population size of the region in years 2030, 2040, and 2050.
Show only the whole number part of the result.
f)
Using the same model, estimate the year in which the population will reach the 50 and 60 million
milestone. Show only the whole number part of the result.
A. Population Growth Model:
Part II. Using a desmos, construct an exponential model that follows the form of either y = A(B)* or y = Aerx.
B. Exponential Model:
Part III. Use the two models (population growth model and exponential model) to estimate the population size of the
region assigned to you in years 2030, 2040, and 2050. Show only the whole number part of the result.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Compute the difference and the rate of frowth.
VIEW Step 2: Find the annual relative growth rate.
VIEW Step 3: Find the exponential model and estimate the population of the year 2030,2040,2050.
VIEW Step 4: Estimate the year in which the polulation will reach 50 million and 60 million.
VIEW Step 5: Construct an exponential model in Desmos and estimate the population in the year 2030,2040,2050.
VIEW Solution
VIEW Step by stepSolved in 6 steps with 1 images

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